A novel mathematical model for single-phase fluid flow from unconsolidated formations to a horizontal well with the consideration of stress-sensitive permeability is presented. The model assumes the formation permeability is an exponential function of the pore pressure. Using a perturbation technique, the model is solved for either constant pressure or constant flux or infinite lateral boundary conditions with closed top and bottom boundaries. Through Laplace transformation, finite Fourier transformation and numerical inversion methods, the solutions are obtained and the pressure response curves are analyzed. The agreement between the analytical solutions in this paper and the numerical results from commercial software (Saphir) is excellent, which manifests the accuracy of the results derived in this paper.