Laminated composite plates are extensively used in aerospace, military, civil infrastructure, and automotive industries due to their benefits, including superior fatigue resistance, high strength, and lightweight properties. Customizable fiber orientation, materials, and stacking patterns are additional advantages. Therefore, conducting rigorous analyses to evaluate deflections and stress levels in these plates is essential for maintaining structural integrity and optimal performance across various applications. The solutions presented in this study rely on the utilization of a higher-order shear deformation theory (HSDT), which offers a notably precise depiction of the plate's behavior. The theoretical model employed in this research accounts for deformations and the variation of stresses along the thickness direction. Finite element formulations are employed to derive the solutions. In order to ascertain the accuracy and reliability of the current formulations and solution methodologies, the obtained results are systematically compared with those documented in the existing literature. This rigorous comparison serves as a robust validation of the approach applied in this study. Once the accuracy of the solutions is established, numerical results for two layered cross-ply composites with real material properties are presented. These results are in good agreement with the findings reported in the literature. By incorporating Higher Order Shear Deformation Theory (HSDT), the accuracy of predictions is significantly enhanced. This improvement ensures a more dependable foundation for the design and optimization of composite structures.