The goal of this research has been the development of an effective design tool for torsional analysis. In the hopes of achieving this goal the computer program, Torsion 1, has been created. This torsional transfer matrix program provides the user with the ability to easily model multi-rotor systems using a simple user-interface. The program is capable of modeling such components or system characteristics as continuously distributed mass, viscous and structural damping, vibration absorbers, and gear meshes with gear tooth flexibility. The analysis capabilities of the program include forcedresponse and free-vibration analyses. The forced-response analysis module is capable of determining a system’s response to a static or harmonic torsional load. The free-vibration analysis module allows is capable of determining the eigenvalues and eigenvectors for damped and undamped systems. This thesis includes an explanation of the multi-rotor transfer matrix technique employed in Torsion 1. The derivation of transfer matrices for visco-elastic vibration absorbers, pendulum absorbers, flexible gear meshes, and planetary gear trains are included in this work. Finally, the validity of the program results is verified with a set of benchmark examples.