The availability of the Automated MultiLevel Substructuring (AMLS) software has enabled frequency response analyses using very large FE models and many modes. With certain simplified types of damping the resulting modal matrices can be solved easily. However, modeling damping accurately can make modal frequency response problems computationally very expensive to solve. Accurately modeled damping results in matrices that are fully populated rather than diagonal. The modal frequency response then requires a matrix factorization at each frequency. The time required for each factorization is proportional to the cube of the number of modes, so analyses up to higher frequencies, for which many modes are required, become extremely expensive. FastFRS (fast frequency response solver) addresses this issue by performing only one numerical operation whose cost is proportional to the cube of the number of modes, rather than one such operation at each response frequency. The solver obtains an exact, direct solution, rather than an approximation for which the user specifies a cutoff frequency, a convergence tolerance, or some other parameter requiring special expertise or instruction. As a result, FastFRS is very reliable and easy to use.