In this paper the excitation mechanisms for mechanical oscillations mediated by magnetomechanical coupling in van der Waals antiferromagnets are discussed. It is shown that, in spite of the compensation of direct magnetic field effect due to the presence of two magnetic sublattices in antiferromagnets, the inverse flexomagnetic effect, the electric field-induced gyromagnetic effect, and the magnetostrictive interaction can cause detectable mechanical oscillations due to the phenomena of forced or parametric resonance. The results of analysis demonstrate the potential of such materials as a basis for new-generation of controllable micro- and nanomechanical systems, they are also of interest from a methodological point of view as an application of classical methods of oscillation theory, such as the harmonic balance method and slowly varying amplitude approximation, to analyze phenomena discovered in van der Waals magnets in the past few years.