In this paper, stability and mechanistic simulations for a four-beam-mass-based MEMS gravimeter were conducted, and guidelines for the gravimeter design were proposed. Based on a prototyped MEMS device, the nonlinear finite element model was validated first against the experimental results. Then, we demonstrated three different scenarios in design that have three distinct modes of deformation: the mode with buckling (case 1), the mode without buckling but with a single zero-stiffness point (case 2), and the mode without both buckling and zero-stiffness point (case 3). Both case 1 and case 2 presented an unstable and sensitive region, in which a tiny perturbation could result in a rapid increase of the resonance frequency. Case 3, on the other hand, could provide a stable and low resonance frequency with a linear relationship between the displacement and gravitational acceleration. An optimized design of a beam/spring-mass-based relative gravimeter could be achieved using the above guidelines.