In this thesis, we focus on MEMS solid-wave gyroscopes operated in rateintegrating mode. In parallel to the miniaturization efforts of shell-type resonators, we address design and fabrication problems by analysis and simulation. We investigate vibrations of axisymmetric resonators using a shell theory and 2.5D elasticity. We employ classical finite element method and spectral methods. We describe effects of geometric imperfections on gyroscope dynamics and use mode-coupling to model vibration sensitivity. We also detail computations of temperature sensitivities of gyroscope parameters. We then formulate and solve example shape optimization problems based on these analyses. Lastly, we introduce thermomechanical noise squeezing to reduce angle random walk.