The present work aims to study the design and analysis of functionally graded layered sandwich beam with viscoelastic core (Polyethylene terephthalate) in high thermal environment. The top layer is functionally graded material (Ceramic S3N4) and stainless steel on the bottom. The report is divided into five chapters. First two chapters give Introduction and Literature survey of various viscoelastic core with Functionally graded material (FGM) that have unique and different properties from any other material. Materials and Methods used are given in chapter three. Chapter four provides details of ANSYS Software where the sandwich beam is subjected to axial dynamic loaded conditions. The viscoelastic core (Polyethylene terephthalate) layers is observed to be at high temperature but other layer of the beam are at normal conditions. The temperature variation is non-linear in viscoelastic core (Polyethylene terephthalate). The effect of various system parameters such as core thickness ratio, compression, expansion, modal structure test, thermal test are analyzed using ANSYS software. The thickness of beam is responsible for their displacement and boundaries for stable and unstable region are considered in this work. It is found that the buckling load of the beam decreases with increase in core thickness parameter, and temperature of top face of functionally graded material. Temperature variation along thickness has negligible effect on buckling load as well as on natural frequency. In this study as frequency of the beam increases deformation starts first in Polyethylene terephthalate layer of the beam. The instability of the beam increases with increase in core thickness parameter and temperature of the top layer.