In the current study, first-order shear deformation theory is presented for the investigation of the sandwich structure with the FGM face sheet. The equivalent properties of the graded face of the structure are estimated via the rule of mixture technique. The eigen frequency equation obtained via variational method subsequent isoperimetric displacement with finite element technique. The convergence criteria and validation test of the adopted simulation method have been measured by solving the adequate number of numerical examples. The desired frequency responses are obtained under the influence of various structural parameters core to face thickness ratio, aspect ratio, side-thickness ratio, and end constraints condition.