An analytical procedure is developed to solve the magnetohydrodynamic equations for the stellar wind problem in the strong-magnetic field, optically thick limit for hot stars. The slow-mode, Alfven, and fast-mode critical points are modified by the radiation terms in the force equation but in a manner that can be treated relatively easily. Once the velocities at the critical points and the distances to the points are known, the streamline constants are determined in a straight-forward manner. This allows the structure of the wind to be elucidated without recourse to complicated computational schemes