The case of inflow to an aquifer or porous medium inhibited by the presence of a semipervious (clogging) layer is investigated. The flow process is characterized by transient, free surface flow conditions. Here, unlike in previous studies, the nonlinear Boussinesq equation is considered. The influence of the clogging layer is simulated by imposing a nonlinear Robin (third kind) boundary condition at the edge of the aquifer. A semianalytical solution was derived by using the Adomian decomposition method, whose validity was checked by solving the problem by a finite difference method. By adopting a nondimensional analysis, the hydraulic behavior of the investigated problem was presented also in tabular form. Potential application examples are the study of water body-aquifer interactions and the hydraulic processes inside a permeable dam with a semipervious core.