The present work aims at the study of parametric instability of temperature dependent FGM plate with various boundary conditions under an in plane pulsating force. The FGM plate is modelled with a four noded rectangular element using the finite element method. The temperature is assumed to be constant on the surface plane of the plate and varies along the thickness direction. The material properties vary according to a simple power law distribution in terms of the constituent’s volume fraction. Based on Bololtin’s method, a set of second-order ordinary differential equations with periodic coefficients of Mathieu–Hill type is formed to determine the instability regions for FGM plate in high temperature environment. Natural frequency and critical buckling analysis are also discussed as splitting up problems. Numerical results are presented in both dimensionless parameters and graphical forms for temperature dependent FGM plates made of steel and alumina. The affects of temperature, dynamic component of axial force and boundary condition on the instability regions of the temperature dependent FGM plate are investigated and discussed.