This paper presents a mathematical model and a finite element model to investigate the model parameters of mechanical dither in a ring laser gyroscope in which the bimorph piezoelectric actuator are employed as driving mechanisms to avoid the problem of so-called lock-in effects. The validity and efficiency of the mathematical model and finite element model are conformed by comparing with the sinusoidal experimental results, and the errors are 3.14% and 1.79% respectively. Moreover, the parametric design for the geometric dimensions of mechanical dither and the bimorph piezoelectric actuators is easily achieved through finite element model. It is shown that careful selection of the structural parameters allows the resonant frequency to be suitable. These results are important for the mechanical dither design and improvement of high accuracy ring laser gyroscopes and inertial navigation system.