A structure with periodic dynamic load may lead to dynamic instability due to parametric resonance. In the present work, the dynamic stability analysis of laminated composite and sandwich plate due to in-plane periodic loads is studied based on recently developed inverse trigonometric zigzag theory (ITZZT). Transverse shear stress continuity at layer interfaces along with traction-free boundary conditions on the plate surfaces is satisfied by the model obviating the need of shear correction factor. An efficient C^{0} continuous, eight noded isoparametric element with seven field variable is employed for the dynamic stability analysis of laminated composite and sandwich plates. The boundaries of instability regions are determined using Bolotin's approach and the first instability zone is presented either in the nondimensional load amplitude–excitation frequency plane or load amplitude–load frequency plane. The influences of various parameters such as degrees of orthotropy, span-thickness ratios, boundary conditions, static load factors, and thickness ratios on the dynamic instability regions (DIRs) are studied by solving a number of problems. The evaluated results are validated with the available results in the literature based on different deformation theories. The efficiency of the present model is ascertained by the improved accuracy of predicted results at the cost of less computational involvement.