Inspired by the outstanding performance of the hemispherical resonator gyroscopes (HRG), MEMS gyroscopes with circularly symmetric structures are a promising candidate for the next generation of high-performance, cost-effective gyroscopes. However, scaling down to MEMS poses certain performance-limiting challenges: increased sensitivity to inevitable fabrication imperfections and environmental variations, chiefly stress and temperature, that perturb the gyroscope’s ideal modal space and result in quadrature/in-phase errors and, more importantly, long-term drift. Understanding these limiting factors is imperative for harnessing the full potential of circular MEMS gyroscopes. This thesis approaches this objective through an analytical modeling viewpoint. Here, “analytical” is meant to connote an approach based on the physics underlying the gyroscopes’ operation as described by the variational principles of solid mechanics. For the experimental evaluations, we use our fabricated double-ring vibrating ring gyroscope (VRG) (3.2 mm-diameter, 57-59 kHz) and 10-ring disk resonator gyroscope (DRG) (3.4 mm-diameter, 41 kHz). We start by calculating the mode shapes of the entire structure of multi-ring gyroscopes in the presence of structural imperfections and elastic anisotropy. By deriving the gyroscope’s nonideal drive-sense transfer function matrix, we provide rigorous definitions for the quadrature and in-phase outputs, highlighting the role of angular gain, frequency split, mode shape rotations, and quadrature leakage into the in-phase due to the sense mode’s phase error. Next, we present a model for the effects of mechanical stresses leading to the concept of stress stiffness, an additional stiffness induced by such stresses through geometric nonlinearity. We carry out an eigenvalue perturbation analysis to obtain the frequency shifts, mode shape rotations, and quadrature/in-phase errors generated by the stress stiffness. Taking advantage of the circular geometry, we have equipped our ring gyroscopes with 16 capacitive stress sensors located 45◦-apart (eight inside and eight outside the main ring), which pick up the local stress at the substrate level. We present an interpolation scheme to reconstruct the substrate’s stress field using the outputs of the stress sensors, providing us with the mechanical stresses responsible for the stress stiffness in the silicon layer. We validate the model based on PCB bending tests. We finally set out a modeling framework for temperature effects in ring gyroscopes. Our temperature experiments gave temperature coefficient of frequencies (TCFs), such as -10 ppm/◦C and -14 ppm/◦C, that are considerably different than the TCF value ~-30 ppm/◦C expected from the ~-60 ppm/◦C temperature dependency of Young’s modulus of silicon. The model revolves around the engendered stiffness and opposing interaction of two fundamental mechanisms of temperature effects: changes in material properties and thermal stresses. The model demonstrates remarkable efficacy in accurately predicting the TCF and sheds light on residual stresses’ role in forming frequency-temperature hysteresis loops. Considering the great potential of integrating stress with temperature for the long-term performance improvement of MEMS gyroscopes, the results of this thesis serve as a building block toward physics-informed drift compensation algorithms.