This study represents a numerical research in vibration and buckling of functionally graded material (FGM) beam comprising edge crack by using finite element method (FEM) and multilayer perceptron (MLP). It is assumed that the material properties change only according to the exponential distributions along the beam thickness. FEM and MLP solutions of the natural frequencies and critical buckling load are obtained of the cracked FGM beam for clamped–free (C-F), hinged–hinged (H-H), and clamped–clamped (C-C) boundary conditions. Numerical results are obtained to show the effects of crack location (c/L), material properties (E2/E1), slenderness ratio (L/h) and end supports on the bending vibration and buckling properties of cracked FGM beam. The FEM analysis used in this paper was verified with the literature, and the fundamental frequency ratio (w) and critical buckling load ratio (Pcr) results obtained were compared with FEM and MLP. The results obtained are quite compatible with each other.