Interfacial stress singularity in a unidirectional two-dimensional laminate model consisting of an elastic fiber and a viscoelastic matrix has been investigated using the time-domain boundary element method. First, the interfacial singular stresses between the fiber and the matrix of a unidirectional laminate subjected to a uniform transverse tensile strain have been investigated near the free surface, but without any defect or any edge crack. Such a stress singularity might lead to fiber-matrix debonding or interfacial edge cracks. Then, the overall stress intensity factor for the case of a small interfacial edge crack of length a has been computed.