A one-dimensional analytical model for axial deformation of continuous fiber reinforced metal-matrix composites under both thermal cycling and isothermal creep, with or without externally applied stresses, has been developed. Fibers in the model are considered to be non-creeping, therm-elastic solids, whereas the matrix is considered to be thermo-elastic-plastic and creeping. The model accounts for the strain history of the composite, and allows for changing matrix creep mechanisms via the use of unified creep laws. The use of unified creep laws allows separation of the overall instantaneous creep strain rate into dislocation creep and diffusional creep components, which can be further separated into power law breakdown, pipe diffusion controlled power law, volume diffusion controlled power law, Coble and Nabarro-Herring creep. Additionally, the model allows for the incorporation of time-dependent interfacial sliding near the extremities of the fiber due to the existence of interfacial shear stresses. Based on a recent study, interfacial creep has been represented as being controlled by diffusional flow with a threshold stress (Bingham flow). The interfacial creep law allows simulation of non-isostrain deformation across the interface, and thus the model is capable of explaining experimental observations of strain incompatibility across the interface near fiber-ends. It is envisioned that such a model will be useful in discerning the predominant matrix creep mechanism at a variety of time periods for a given applied stress and temperature, and thus make it possible for the generation of transient deformation mechanism maps for composites.