A graph-theoretic formulation to perform sensitivity analysis on multibody systems is presented in this article. In this formulation, linear graphs are used to capture the system topologies from which a graph-theoretic formulation simultaneously generates the system equations and the sensitivity equations. This ensures the automated, accurate, and efficient generation of sensitivity equations. The basic formulation steps are outlined to illustrate the process of the generation of sensitivity equations. The salient aspects of multibody systems are presented along with a brief description of the software platform that has been used to implement the algorithm. A 3D pendulum and a double-wishbone suspension system are analyzed to demonstrate the application of the algorithm. The results are validated by using a finite difference formulation. Finally, the efficiency of the software implementation is assessed by comparing the computational costs associated with the proposed method and that of existing methods.