In this paper, a unit cell based micromechanical model is presented to predict the elastic-viscoplastic response of aligned short fiber titanium matrix composites subjected to combined axial loading in the presence of fiber/matrix interfacial damage. The effects of manufacturing process thermal Residual Stress (RS) are also included in the analysis. The representative volume element (RVE) of the short fiber composites consists of c×r×h cells in three dimensions in which a quarter of the short fiber is surrounded by matrix sub-cells. In order to obtain elastic-viscoplastic curves, the fiber is assumed to be linear elastic, while the matrix exhibits elastic-viscoplastic behavior. The Evolving Compliance Interface (ECI) model is employed to analysis interface damage. This model allows debonding to progress via unloading of interfacial stresses even as global loading of the composite continues. Results revealed that for more realistic predictions, in comparison with available experimental and the other models results, both interfacial damage and thermal residual stress effects should be considered in the analysis.