We performed a numerical simulation of a time-dependent interfacial failure accompanied by a fiber failure, and examined their evolution under shear and compressive loads in single-fiber composites. The compressive load on the interface consists of Poisson’s contraction for matrix resin subjected to longitudinal tensile load. As time progresses, compressive stress at the interface in the fiber radial direction relaxes under the constant longitudinal tensile strain condition for the specimen, directly causing the relaxation of the interface frictional stress. This relaxation facilitates the failure of the interface. In this analysis, a specific criterion for interface failure is applied; apparent interfacial shear strength is enhanced by compressive stress, which is referred as quasi-parabolic criterion in the present study. The results of the stress recovery profile around the fiber failure and the interfacial debonding length as a function of time simulated by the finite element analysis employing the criterion are very similar to experimental results obtained using micro-Raman spectroscopy.