<p>This study presents a comprehensive investigation into the dynamic stability analysis of laminated composite plates using meshless methods, particularly the Radial Point Interpolation Method (RPIM). Laminated composite plates are widely utilized in civil and aerospace engineering due to their exceptional properties, including high strength-to-weight ratios, lightweight nature, and tailorable anisotropic behavior. However, analyzing their dynamic stability poses significant challenges due to geometric nonlinearities and critical responses under time-varying loading conditions. In this research, RPIM is integrated with higher-order shear deformation theories, specifically the Third-Order Shear Deformation Theory (TSDT) and Classical Plate Theory (CPT), to model complex plate behaviors under diverse dynamic loadings, such as periodic, moving, and combined loads. The influence of critical parameters, including fiber orientation, number of layers, thickness-to-width ratio, boundary conditions, and elastic modulus ratio, on the primary dynamic instability region is thoroughly examined. The results demonstrate that the combination of RPIM and TSDT yields highly accurate predictions of natural frequencies and critical buckling loads, particularly for thick plates where shear deformation effects are pronounced. The primary innovation lies in a robust computational framework leveraging meshless methods for greater geometric flexibility and computational efficiency; benchmark tests show RPIM achieves ~ 20–30% faster computation than FEM for comparable accuracy. Increasing the length-to-thickness ratio and elastic modulus ratio shifts the dynamic instability region to higher excitation frequencies, enhancing structural stability. This work advances the understanding of nonlinear dynamic stability phenomena in laminated composites and offers a robust computational framework for future studies in structural mechanics.</p>