This paper analyses the root causes of zero-rate output in MEMS vibratory gyroscopes. Zero-rate output is one of the major challenges for high performance gyroscopes. The knowledge of its causes is important to minimize zero-rate output and achieve a robust sensor design. In this paper, a new method to describe a MEMS gyroscope with a parametric state space model is introduced. The model is used to theoretically describe the behavioural influences. A new, more detailed and general gyroscope approximation is used to vary influence parameters, and to verify the method with simulations. The focus is on varying stiffness terms, and an extension of the model to other gyroscope approximations is also discussed.