Functionally graded materials (FGMs) are engineered in such a way that their properties vary gradually over the volume. The non-homogeneous nature of FGM can be beneficial in many real-world applications if its behavior can be predicted for critical conditions. This paper studies the free vibration analysis of FGM plates for various thickness ratios using the first-order shear deformation theory (FSDT), in which the equations of motion are derived through Hamilton’s principle, and Navier’s solution provides the boundary conditions. The findings, derived from numerical simulation in ANSYS and MATLAB analyses of sandwich FGM plates, reveal the dependency of natural frequencies on the core volume fraction. The present study focuses on symmetric and non-symmetric FGM plates about the mid-plane in the 1-1-1, 1-2-1, 2-1-1,2-1-2, 1-0-1, and 2-2-1 thickness ratios and aims to validate the frequency parameter results derived through numerical and analytical approaches using FSDT with classical plate theory (CPT). The paper examines how variations in material composition and plate geometry influence free vibration frequencies and mode shapes contributing to failure analysis of FGM plates. The present study concludes that variations in the thickness ratio and volume fraction index significantly impact frequency parameters.