The stability and synchronous rotation of oscillators is a key technology of the sonic drilling rigs, vibratory breakers and pile sinkers. This paper studies the stability and synchronization properties of two oscillators in a solid–liquid coupling system. The system mainly comprises two oscillators, two hydraulic motors and a gear pair. Since each oscillator is driven by a hydraulic motor and the hydraulic motors are connected in parallel, a new dynamic model of the two oscillators is established. In this model, we consider both the nonlinearity of the gear pair and the hydraulic factors. According to the numerical results, the new method improves the stability of the system. The rotational angle and speed deviations indicate that the system can guarantee the synchronization of the two oscillators when the meshing stiffness and meshing damping ratio of the gear system are varied. The synchronization accuracy is excellent. Additionally, the numerical results are validated by simulation in AMESIM software.