Abstract: Based on the theory of elastic dynamics, the scattering of elastic waves and the dynamic stress concentration in a fiber-reinforced composite are studied. The non-homogeneous region of interlayer is modeled to have many same-thickness layers with elastic properties. Analytical expressions of elastic waves in different medium regions are presented. The unknown coefficients of elastic waves are determined in accordance with the continuous conditions of displacement and stress on the boundary of the interfaces. The expressions for calculating the dynamic stress concentration factors are given. As examples, the numerical results of dynamic stress concentration factors near the interfaces of two kinds of fiber-reinforced composites, namely, SiC-fiber-reinforced Ti composite and Al₂O₃-fiber-reinforced Al composite, are calculated. The influences of material characters and structural size on the dynamic stress concentration factors near the interfaces of these two kinds of composites are analyzed.