Summary: A variational method is developed for analyzing the matrix creep induced time-dependent change in fiber stress profiles in unidirectional composites. A functional of admissible profiles of fiber stress rate is presented by supposing a fiber broken in matrix as well as a fiber pulled out from matrix. The functional is shown to have the stationary function satisfying an incremental differential equation based on the shear lag assumption. Then, the stationary function is approximately determined by assuming bilinear profiles of fiber stress and a power law of matrix creep, leading to analytical solutions for the time-dependent change in fiber stress profiles. The solutions are verified on the basis of an energy balance equation and a finite difference computation. Moreover, it is shown that the solution for the fiber pull-out model agrees well with an experiment on a single carbon fiber/acrylic model composite if the initial slip at fiber/matrix interface is taken into account. In addition, the solution for the fiber breakage model is used for evaluating the characteristic time in long-term creep rupture of unidirectional composite.