A popular type is of metal matrix reinforced by ceramics particles. It has been revealed that the composites are susceptible to interfacial degrading, which may be dramatically detrimental to the overall properties of composites. In present paper, an equivalent inclusion type constitutive model was developed for the composites with dispersed particles on which imperfections of the material interface are incurred. Two fundamental tensors are derived, the modified Eshelby tensor and the damage tensor of the weakened particles. By applying these tensors into a carefully schemed constitutive law, the effects of interfacial degrading on the overall properties of composite materials can be investigated. The interface degrading includes sliding and debonding. The numerical results show that even with the nil resistible sliding coefficient, its effect on the overall Young’s modulus is not notable unless the volume fraction of the particle is so high as more than 70%. For the global Poisson’s ratio, when there is the sliding on the interface, the Poisson’s ration rises irrespective of the constituent material values. It is noted that even in the elastic state, the global Poisson’s ratio rises greater than that of both the constituents. This phenomenon might indicate that even at the elastic state, the particle interfacial sliding would give somewhat a plasticity-like deformation behavior. The effect of the interfacial debonding on the overall properties of the composite is more conspicuous in comparisons of the sliding. The debonding parameter greatly affects both the properties for almost entire range of the particle volume fraction. Unlike the sliding effect case, the debonding decreases Poisson’s ratio at all cases, which represents the micro-damage effect occurring in the composite.