The focus of this investigation was to computationally determine the vibrational characteristics of a rear fuselage mounted aircraft engine support frame. A pseudo-orthogonality check was performed to compare the computational results with experimental data. This produced a matrix with 8 modes with diagonal terms >0.9. Structural modifications were made to the computational model of the frame in order to decrease the modal density near the blade pass frequency of the engine at cruise conditions. Two independent modifications to the frame decreased the modal density within 1% of the critical engine frequency from seven to five and four respectively. It was shown that the modifications produced non-intuitive results, as each modification had a different significance in terms of how it affected each mode of the system. It is recommended that computational analysis be performed on similar structures before such modifications are put in place, as there is low predictability of how different modifications will affect the modal properties of the system.