Dynamic model of the transmission system of non-sinusoidal oscillation driven by elliptical gears is built. And the differential equations of motion are deduced. The results suggest that the mass matrix

the stiffness matrix and the damping matrix of the transmission system vary with the configuration of the crank. It’s a dynamic system with periodic time-varying parameters. Periodic solutions are gained by means of harmonic balance method. Also the dynamic stability of the solutions is considered. Based on the distinct characteristic exponent assumption and the Floquet theory

the formula to gain the characteristic exponent is deduced. From the characteristic exponents

the stability can directly be read. A solid foundation for solving the running smooth problem of the mold and for better applying of the oscillation device is provided.