Image Analysis & Segmentation

ITK_SNAP is a software application used to segment structures in 3D medical images (GPL license, see http://www.itksnap.org).
Slicer is a free, open source software package for visualization and image analysis (BSD-style open source license, see http://www.slicer.org).
MITK, The Medical Imaging Interaction Toolkit is a free open source software platform aimed at providing support for an efficient software-development of methods and applications dealing with medical images (BSD-style license, see http://www.mitk.org).
SimpleITK is a simplified layer built on top of ITK to facilitate its use in rapid prototyping of image analysis that can be used in interpreted languages, e.g. Python, (Apache 2.0 License license, see http://www.simpleitk.org/).
C3D is a command-line tool for converting 3D images between common file formats, which also includes a growing list of commands for image manipulation, such as thresholding and resampling (GPL license, see http://www.itksnap.org/pmwiki/pmwiki.php?n=Downloads.C3D).

Geometry & Mesh Generation & Manipulation

SALOME is an open-source software that provides a generic platform for pre- (cad, meshing) and post-processing for numerical simulation (LGPL license, see http://www.salome-platform.org/).
- Learn how to easily add python libraries to Salome here.
Gmsh is a free 3D finite element grid generator with a build-in CAD engine and post-processor. Its design goal is to provide a fast, light and user-friendly meshing tool with parametric input and advanced visualization capabilities. (GNU General Public License (GPL license, see http://gmsh.info/)
FreeCAD is an open-source three-dimensional computer aided design software (GPL and LGPL licenses, see http://www.freecadweb.org/).
MeshLab is an open source, portable, and extensible system for the processing and editing of unstructured 3D triangular meshes (GPL license, see http://meshlab.sourceforge.net/).
OpenFlipper is an OpenSource multi-platform application and programming framework designed for processing, modeling and rendering of geometric data (LGPL license, see http://www.openflipper.org/).
PyGTS is a Python binding for the GNU Triangulated Surface (GTS) Library to construct, manipulate, and perform computations on 3D triangulated surfaces, including boolean operations (GPL license, see http://pygts.sourceforge.net/).
pyFormex provides a wide range of operations on surface meshes, such as STLs; the software can also be used as a pre- and post-processor for Finite Element analysis programs (GPL license, see http://www.nongnu.org/pyformex).
IA-FEMesh is freely available, interactive, structured hexahedral mesh generation software relying on surface projection method (BSD style license, see http://www.ccad.uiowa.edu/MIMX/projects/IA-FEMesh).
Blender is the free and open source 3D creation suite, which supports the entirety of the 3D pipeline, including: modeling, rigging, animation, simulation, rendering, compositing, motion tracking, video editing, and game creation. (GPL license, see https://www.blender.org/).

Scripting & Numerical Analysis

Python is a programming language (GPL compatible license, http://www.python.org/). Python is the default scripting environment for Multis.
- SciPy is a Python based open-source software for mathematics, science, and engineering (BSD license, see http://www.scipy.org/).
- matplotlib is a python 2D plotting library which produces publication quality figures in a variety of hardcopy formats and interactive environments across platforms. The pyplot interface provides a MATLAB-like interface. (PSF license, see http://matplotlib.org/).
- npTDMS is Cross-platform, NumPy based module for reading TDMS files produced by LabVIEW. TDMS files are the binary files used for the robotic testing raw data. (LGPL license, see https://pypi.python.org/pypi/npTDMS/).
- numpy-stl makes working with STL files easy (https://pypi.python.org/pypi/numpy-stl)
- PyGeM is a python library using Free Form Deformation and Radial Basis Functions to parametrize and morph complex geometries. (MIT license see https://github.com/mathLab/PyGeM)
- PyGTS is a Python binding for the GNU Triangulated Surface (GTS) Library to construct, manipulate, and perform computations on 3D triangulated surfaces, including boolean operations (GPL license, see http://pygts.sourceforge.net/).
- pyFormex provides a wide range of operations on surface meshes, such as STLs; the software can also be used as a pre- and post-processor for Finite Element analysis programs (GPL license, see http://www.nongnu.org/pyformex).
Anaconda is an easy-to-install free package manager, environment manager, Python distribution, and collection of over 720 open source packages (https://docs.continuum.io/anaconda/)
Spyder is an interactive development environment for Python with advanced editing, interactive testing, debugging and introspection features (MIT license, see http://code.google.com/p/spyderlib/).
PyCharm is a integrated development environment for Python. The free community version include code completion and debugging. (https://www.jetbrains.com/pycharm/)

Finite Element Analysis

FEBio is a nonlinear implicit FE framework designed specifically for analysis in biomechanics and biophysics (Custom open source license; free for research use, licensing for commercial use is available, see http://www.febio.org).
SOFA the Simulation Open Framework Architecture is an open-source software primarily targeted at real-time simulation, with an emphasis on medical simulation (LGPL license, see https://www.sofa-framework.org).
Code_Aster is free and open source software package for numerical simulations in structural mechanics (GPL license, see http://www.code-aster.org).