A general framework has been developed to investigate dynamic stability of composite plates under dynamic and static compressive loads. A variationally consistent, higher-order shear deformation theory has been used to model the displacement field. The linear strain-displacement relationship corresponding to the small deformation assumption is used first. Both transverse shear and rotary inertia effects are taken into account. The mathematical model is implemented using the finite element approach. The impact of delamination on the natural frequencies, critical buckling load, and instability regions is investigated Parametric studies are conducted to investigate the influence of delamination placement and size, boundary conditions, plate thickness, static pre-stress, and stacking sequence on the instability regions. Finally, the importance of geometric nonlinearity is studied by introducing von Karman nonlinearity. Natural frequency results are obtained for square isotropic and cross-ply laminates and compared with available analytical data. The effect of geometric nonlinearity on the principal instability region is also investigated for cross-ply laminates.