The use of finite elements for simulation of rotor systems has received considerable attention within the last few years. The published works have included the study of the effects of rotatory inertia, gyroscopic moments, axial load, and internal damping; but have not included shear deformation or axial torque effects. This paper generalizes the previous works by utilizing Timoshenko beam theory for establishing the shape functions and, thereby including transverse shear effects. Internal damping is not included but the extension is straight forward. Comparison is made of the finite element analysis with classical dosed form Timoshenko beam theory analysis for nonrotating and rotating shafts.