Abstract: The effect of diffusion controlled interfacial sliding on the transverse shear deformation of fibrous composites is studied. The matrix and fiber are assumed elastic, and the sliding rate is proportional to the shear stress on the interface. As an auxiliary problem, the special case of a single fiber embedded into an infinite matrix is considered firstly, and the time dependent stress in the composite at any time is given. The overall response of the composite is then analysed by Mori-Tanaka method. Numerical results reveal that the transverse shear modulus of the composite decreases significantly with the occurrence of interfacial sliding.