Based on a new definition of effective stress introduced by Qiu and Weng (1992) for a heterogeneously deformed matrix, and the use of elastic-creep secant moduli to characterize the weaking constraint power of the ductile matrix, a theory is proposed to estimate the development of tensile creep strains of a fiber-reinforced metal-matrix composite, and to examine the evolution of maximum interfacial tensile stress under transverse loading. The effective stress is defined in terms of the distortional energy of the matrix of a linearly elastic comparison composite, and, since the contribution of the locally perturbed deviatoric stress is accounted for, the theory can be applied to a concentration level which is higher than the traditional mean-field approach. Consideration of the weakening constraint power in the creep matrix also permits the theory to be applied to a somewhat greater range of creep strain as compared to the method of elastic constraint, which is suited only when the creep strain is about of the same order, or even less, of the elastic strain. The calculated axial creep, transverse tensile creep, and bi-axial tensile creep for the Borsic/aluminum composites indicate that the overall creep response of the system is indeed softer than those calculated by the elastic-constraint approach. The interfacial tensile stress under a transverse tension, and under a combination of transverse tension and lateral compression, is shown to grow continuously, leading to potential interfacial debonding under long-term creeping condition.