In this article, the bending, buckling, free and forced vibration behavior of a nonlocal nanocomposite microplate using the third order shear deformation theory (TSDT) is presented. The magneto-electro-elastic (MEE) properties are dependent on various volume fractions of CoFe2O4-BaTiO3. According to Maxwell’s equations and Hamilton’s principle, the governing differential equations are derived. These equations are discretized by using Navier’s method for an MEE nanocomposite Reddy plate. The numerical results show the influences of elastic foundation parameters such as aspect ratio, length to thickness ratio, electric and magnetic fields and various volume fractions of CoFe2O4-BaTiO3 on deflection, critical buckling load and natural frequency. The natural frequency and critical buckling load increases with the increasing volume fraction of CoFe2O4-BaTiO3, also the amplitude vibration decreases with an increase in the volume fraction. This model can be used for various nanocomposite structures. Also, a series of new experiments are recommended for future work.