Functionally graded materials are obtained by combining two materials, usually a metal and a ceramic. The metal component provides strength and rigidity, whereas the ceramic component provides resistance against heat. Thus, functionally graded materials not only pose high strength but are also resistant to heat. Due to these properties, functionally graded materials have found immense use in various engineering works. Plates have been used in nearly all areas of engineering. A plate structure has to primarily resist bending and shear stresses. When plates are used in engineering works, where lot of heat is produced, it becomes necessary to make them not only strong, but also heat resistant. Sometimes, presence of cutouts cannot be avoided due to repair, ventilation or other purposes. Depending on the size, shape, and position of cutouts, presence of cutouts can result in significant changes in plate behavior. Hence a functionally graded plate with eccentric circular cutout has been used for analysis. The dynamic free vibration has been studied based on Mindlin’s first order shear deformation theory (FSDT). Eight-noded serendipity isoparametric elements have been applied in the finite element analysis. Parametric studies have been performed to show the effect of material, power law index, boundary conditions, and thickness on the natural frequency of functionally graded plate. It is shown that the obtained frequencies considerably depend on the mentioned parameters. All analyses have been performed using MATLAB.