The research focus on sandwich beam which is graded material as containing in high thermal environment. The aim of this work to find out the stability of dynamic and free vibration for sandwich beam. Here main advantage of the sandwich beam as top layer of functionaly graded material and stainless steel on the bottom.Functionally graded material (FGM) belongs to advanced type material that have unique and different properties from any other material.This sandwich beam is subjected to axial dynamic loaded condition and the layer is having high temprature but other layer of the beam is normal (room temprature). The variation of the temprature in the sandwich beam are linear and non linear. The model of beam is assiocated with FEM and beam element has four degree of freedom and rotation in case of degree of freedom are longitudnal displacement. The thickness of beam are responsible for there displacement and boundries for stable and unstable region are considered in this work. In this study the frequency of the beam also decreases with increase in the thickness parameter, power loe index and temprature. The instability of the beam increases with increase in core thickness parameter, power low index and temprature of the top layer.