In this present study, the dynamic characterization and instability analysis of a rotating composite magnetorheological fluid sandwich plate under periodic in-plane loading are investigated. The governing differential equation of motion of a rotating composite magnetorheological fluid sandwich plate is derived based on classical laminated plate theory and presented in the finite element formulation. The effectiveness of the developed finite element formulation is demonstrated by comparing the results in terms of natural frequencies and parametric resonance frequencies available in literature. Various parametric studies are performed to investigate the influences of magnetic field intensity, setting angle and rotating speeds on the variation of natural frequencies and instability regions of rotating laminated composite magnetorheological fluid sandwich plate under periodic in-plane loading. It can be observed that the natural frequencies increase with increase in rotating speed and magnetic field irrespective of the modes considered. It can also be observed that the effect of variation in setting angle of non-rotating magnetorheological elastomer sandwich plate on the buckling load is minimal at various magnetic fields. However, it is observed that the buckling load increases with increase in magnetic field. Further, it can be observed that normalized width of principal and secondary instability regions decreases with increase in rotating speed and magnetic field considered. © The Author(s) 2018.