Most assembled rotor dynamics finite element models result in very large matrices because the structural details are represented with high fidelity. Because the real life operational scenarios also require the solution of the dynamic equations in a wide range of rotational speeds, the accuracy and efficiency of the solution techniques employed are of utmost importance. This chapter mainly focuses on the computational aspects of the solution of the equations developed in the last chapter. The accuracy aspects of the numerical solution of the equations are the topic of the next chapter.