Many piezoelectric microelectromechanical systems (MEMS) measure or generate acoustic signals via the motion of radially non-uniform, thin film composite plates. The composite layers provide piezoelectric actuation, structural support, electrode metallization, passivation, etc. Often, the layers are non-uniform over the plate and contain residual stresses introduced during the fabrication process. Accurate models of non-uniform composite plate mechanics are crucial for predicting and optimizing device performance. In this paper, an analytical solution for a radially non-uniform, piezoelectric, circular composite plate incorporating residual stress is derived. The analytical solution is compared to experimental measurements of a MEMS piezoelectric diaphragm. The results show the improved accuracy of the analytical model when including film stress, the speed of the analytical solution as compared to finite element analysis, the sensitivity of device performance to residual stress and the importance of accurate film stresses as model inputs. The analytical model presented is useful as a design optimization tool given the efficiency of the computational time, shown to be 275 times less than a comparable finite element analysis.