Abstract In this study, consider a Timoshenko beam based on the functionally graded material, to analyze the natural frequency with several different materials. First , we derive the equations of motion and boundary conditions by Hamilton's principle, and then use the Galerkin's Method to reduce the equations of motion to ordinary differential equations, then apply Runge-Kutta method to obtain the Relationship of amplitude ratio verse time. Each has a different . Finally compare natural frequency with natural frequency . Keyword: Timoshenko beam, functionally graded material, natural frequency, free vibration