Finite element analysis is a computerized method widely used in industry to model and solve engineering problems relating to complex systems. Perhaps the most common use of finite element analysis is in the field of solid mechanics where it is used to analyze structural problems. To achieve the correct results the component and all mating interfaces must be modeled properly. Previously this was done by performing the analysis, manufacturing a prototype based on this design, and then physically determine the natural frequencies of the prototype attached to the interface structure. Once the actual natural frequencies are determined, the boundary conditions and other modifications of the finite element model are adjusted using a trial and error method until an acceptable correlation with the measured frequencies is achieved. This process is extremely time consuming and CPU intensive because it requires the design and testing of an initial prototype as well as repeated adjustments and resolution of the system equations. This paper will present a method to determine the proper boundary conditions at mating components for accurate first time finite element analysis results. The results that have been achieved analytically have been verified and now approach the limits of test error.