Most of the commercial packages include many different sorts of simulation environments of which FEM software is only one flavor.

• ADINA - Automatic Dynamic Incremental Nonlinear Analysis
• ALGOR
• AxisVM
• ANSYS
• Cast3M
• Cenaero
• Compass - Ram Series, Nastran
• COMSOL - Multiphysics Environment
• COSMOSWorks (from SolidWorks)
• ESI - Systus and other packages
• Europlexus (Samcef)
• FEAT - Finite Element Application Technology
• FEMAP
• FesaWin
• Go-Mesh
• JL-Analyzer (autofea)
• LISA
• LS-Dyna
• MARC - also includes enterprise NASTRAN
• NEi Software - another flavor of NASTRAN
• NISA
• PERMAS
• Pro/Engineer - CAD suite that includes FEM
• Range
• SIMULIA - (formerly Abaqus)
• SolidWorks
• Strand7
• VisualFEA

Source code is not available for all programs.

Blurbs are taken mostly vertbatim from each tool's web site and do not necessarily confer meaningful information or a reccomendation.

• ADVENTURE(ADVanced ENgineering analysis Tool for Ultra large REal world.) - efficient modeling, calculation, and visualization of 3-D models for 10 to 100 million DOF meshes using various parallel and distributed computer environments.
• Aladdin - Aladdin is a computational toolkit for the interactive matrix and finite element analysis of large engineering structures, particularly building and highway bridge structures. Aladdin views finite element computations as a specialized form of matrix computations, matrices as rectangular arrays of physical quantities, and numbers as dimensionless physical quantities.
• ALBERTA - "Adaptive multiLevel finite element toolbox using Bisectioning refinement and Error control by Residual Techniques for scientific Applications. "
• CalculiX - CalculiX is an FEM package designed to solve field problems.
• CMISS - An interactive computer program for Continuum Mechanics, Image analysis, Signal processing and System Identification.
• Code_Aster - Mechanics FEM based solver, Over 1.2 M Lines of code. Documentation in French.
• deal.II - "Differential Equations Analysis Library" - The main aim of deal.II is to enable rapid development of modern finite element codes, using among other aspects adaptive meshes and a wide array of tools classes often used in finite element program
• DOUG - "Domain decomposition On Unstructured Grids" - DOUG is a black box parallel iterative solver for finite element systems arising from elliptic partial differential equations. Used in conjunction with a finite element discretisation code, DOUG will solve the resulting linear systems using an iterative method and provides a range of powerful domain decomposition preconditioners.
• DUNE - Distribute and Unified Numerics Environment - a modular toolbox for solving partial differential equations (PDEs) with grid-based methods. It supports the easy implementation of methods like Finite Elements (FE), Finite Volumes (FV), and also Finite Differences (FD).
• Elmer - Open source finite element software for multiphsical problems.
• FEA(S)T - A collection programs for FEM (FEAT2D/FEAT3D), Parallel Solution (FEAST), imcompressible flow (FEATFLOW), grid editor (DeViSoR).
• FENICS - A collection of tools for automated solution of differential equations. We provide software tools for working with computational meshes, finite element variational formulations of PDEs, ODE solvers and linear algebra. IncludesFFC (Finite Element Compiler for Variational Forms); FIAT (Tabulation of finite element function spaces); Puffin (FEM solver for Octave/Matlab); SyFI (symbolic FEM solver), and others.
• FELIB - "The Finite Element Library" - subroutine library for FEM.
• FElt - The current version of FElt knows how to solve linear static and dynamic structural and thermal analysis problems; it can also do modal and spectral analysis for dynamic problems.
• FELYX - "Finite Element Library eXperiment" - numerically efficient FE calculations.
• FEMLISP - Common Lisp framework for FEM -
• FEM_Object - Smalltalk V FE development environment.
• FEMOCTAVE - This is a very simple FEM package for Octave. It solves second order differential equations in two variables, using first order elements.
• FEMSET - Der Finite-Elemente-"Baukasten" FEMSET stellt die Routinen des Finite-Elemente-Algorithmus im Quellcode zur Verfügung (es ist ein “Baukasten” für die Lehre und für Experimente, keine Konkurrenz für kommerzielle Systeme).
• FFEP -"Free Finite Element Package" - These libraries contain numerical methods required when working with linear and quadratic Finite Elements in two dimensions. FFEP works on GNU/Linux and is portable to every system where the Meta Matrix Library (MEML), which means, LAPACK and BLAS are available. (BSD)
• freeFEM - includes freeFEM, freeFEM+, freeFEM++, freeFEM3D
• Getfem++ - The Getfem++ project focuses on the development of a generic and efficient C++ library for finite element methods. The goal is to provide a library allowing the computation of any elementary matrix (even for mixed finite element methods) on the largest class of methods and elements, and for arbitrary dimension (i.e. not only 2D and 3D problems).
• HMD - an engineering application for FEM.
• Impact - an open source finite element program suite which can be used to predict most dynamic events such as car crashes or metal sheet punch operations. They usually involve large deformations and high velocities.
• IMS - "IMTEK-Mathematica-Supplement"
• kaskade - finite element adaptive mesh code for solving problems in 2D/3D (via MGNET Muligrid mirror).
• KFEM - adapts FreeFem to KDE.
• LUGR - efficient computation of rapidly varying temporal and spatial solution transitions by automatic local grid adaptation.
• MiniFEM - MiniFEM ist ein experimentelles, objektorientiertes Finite Elemente Programmsystem, das ursprünglich im Rahmen einer Studienarbeit am Lehr- und Forschungsgebiet "Mathematische Modelle in der Werkstoffkunde" der RWTH Aachen entwickelt wurde.
• MODFE - Modular finite-element model for areal and axisymmetric ground-water flow problems
• MODULEF - The MODULEF library contains about 3000 procedures written in Fortran 77
• NASTRAN
• NLFET - Nonlinear finite element toolbox for MATLAB.
• OLEFI - Object Finite Element Library - an object oriented library of C++ classes for development of finite element codes
• OOFEM - - OOFEM is free finite element code with object oriented architecture for solving mechanical, transport and fluid mechanics problems that operates on various platforms.
• Open FEM - MiniFEM2D1 - proof of concept application. It does FEM for gridded structures, just what you find as an introductory example in a textbook
• Open FEM (INRIA) - Open Finite Element Toolbox - general purpose muoltiphysics environment.
• OpenSees - FEM for modeling earthquake engineering
• Padfem² - Parallel adaptive finite element framework
• ParaFEM - ParaFEM is a freely available, portable library of subroutines for parallel finite element analysis.
• Rheolef - A finite element environment i.e. some C++ classes and unix commands
• SLFFEA - San Le's Free Finite Element Analysis. It is a package of scientific software and graphical user interfaces for use in finite element analysis.
• Sundance - from Sandia Lab
• TOCHNOG - Open source version of FEAT
• VAPAS - Variational Asymptotical Plate and Shell Analysis (VAPAS) can be used to model composite plates and shells to calculate the generalized two-dimensional stiffness matrices as inputs for two-dimensional plate/shell analysis and recover the 3-D displacement/strain/stress distributions through the thickness.
• VECFEM3 - routines for the numerical solution of 1-D, 2-D and 3-D functional equations over an arbitrary domain using the finite element method.
• WARP3D - research code for the solution of very large-scale, 3-D solid models subjected to static and dynamic loads.
• Z88 - finite element analysis program