A generalized radial flow model, treating the flow dimension as an arbitrary number and taking into account the well skin effect, is presented to describe the transient head distribution in a fractured medium under the Robin condition during constant-head tests. The Laplace-domain solution for the head distribution is first developed via the Laplace transforms; and the corresponding time-domain solution in terms of the hydraulic head is then obtained using the Bromwich integral method. In addition, based on the head solution and Darcy's law, the solution for the wellbore flux is further developed to investigate the skin effect. It is found that the skin effect on the wellbore flux is significant at early times. Under this circumstance, it would not be appropriate to neglect the skin effect in the model in determining the hydraulic parameters from the analysis of field data. Our solutions will be useful for the predictions of the spatial and temporal head distribution and wellbore flux or in investigating the skin effect on the head distribution and wellbore flux for flow with various dimensions in fractured media.