This study investigates strain-rate dependent transverse tensile failure of unidirectional composite materials with a periodic unit-cell simulation. The unit cell consists of 20 fibers aligned at random in the matrix. Elasto-viscoplastic constitutive equation including continuum damage mechanics is used for the matrix. This enables us to simulate strain-rate dependence of matrix plastic deformation and damage. For the fiber/matrix interface, cohesive zone model is also employed. Interface failure under combined stress state of normal and shear is considered. Fibers are assumed to be elastic body. When strain rate is relatively high, naturally, the maximum matrix stress is relatively large due to the viscoplastic properties so that the interface tends to fail in advance of matrix yielding and/or failure. On the contrary, when strain rate is low, the maximum matrix stress becomes small and interface failure does not appear.