Abstract: Based on asymptotic expansion of the out-of-plane displacement of the mode II crack propagating under plane stress conditions at constant velocity in functionally gradient materials, two types of property varia- tions in the direction of crack propagation are analyzed: (1) linear variation of the shear modulus with constant mass density; (2) exponential variations of shear modulus and mass density. The Poisson's ratio is assumed to be constant. The caustics expressions of the mode II stress field around a propagating crack of the two variations are developed. The numerical simulations of the caustics are given and the influences of different gradients to crack behaviors are analyzed. The relation of dynamic stress intensity factors and the size of caustics are obtained.