In this research, analytical and numerical investigation of the ceramic- metal FGM beam under low velocity impact is carried out by first order shear deformation beam theory. The mass and stiffness matrixes are proposed by combination of Energy method, Ritz and Lagrange method. Also, simulating of low velocity impact on the ceramic- metal FGM beam is carried out by ABAQUS software that the beam is divided about 30 layers in thickness direction in ABAQUS software to create a functionally graded beam. Maximum contact force between impactor and beam in analytical model and ABAQUS software are 1062 and 1039 N with 2.21 percent difference and maximum impactor displacement in analytical model and ABAQUS software are 0.0104 and 0.0108 mm with 3.85 percent difference. Finally, the effect of FGM function types include the combination of exponential and polynomial functions, impactor velocity 1, 2 and 3 m/s, impactor radius 8, 12.7 and 16 mm and simply and clamped supported boundary condition are investigated on the contact force and indentation histories. The maximum and minimum contact forces are belonging to first and third order polynomial function and maximum and minimum indentations are belonging to third and first order polynomial function.