This disclosure introduces MBSVT (Multibody Systems at Virginia Tech), as a software library for the kinematic and dynamic simulation of multibody systems, with forward kinematics and dynamics, direct, and adjoint sensitivity analysis, and optimization capabilities. The MBSVT software was developed in Fortran 2003 as a collection of Fortran modules and it was tested on several different platforms using multiple compilers. The kinematic library includes dot-1 constraint, revolute, spherical, Euler, and translational joints, as well as distance and coordinates driving constraints. The forward dynamics uses the penalty formulation to write the equations of motion and both explicit and implicit Runge-Kutta numerical integrators are implemented to integrate the equations. The library implements external forces, such as translational spring-damper-actuator, bump stop, linear normal contact, and basic tire force. Direct and adjoint sensitivity equations are implemented for the penalty formulation. The L-BFGS-B quasi-Newton optimization algorithm is integrated with the library, to carry out the optimization tasks. MBSVT also provides a connection with Matlab by means of the Matlab engine. 3D rendering is available via the graphic library MBSVT-viz based on OpenSceneGraph. The collection of benchmark problems provided includes a crank-slider mechanism, 2D and 3D excavators models, a vehicle suspension, and full vehicle model. The distribution includes a Cmake list, gfortran make files, MSV2010 project files, and a collection of training problems. Detailed doxygen documentation for the MBSVT library is available in html and pdf formats.