Models are calculated for stellar winds driven by radiation pressure in spectral lines. The line transfer equation in the fluid frame is solved in order to evaluate the radiation pressure force, and the hydrodynamic structure is constructed to be consistent with this force. This technique avoids use of the Sobolev approximation, which is not applicable for low flow velocities. The models either use a number of driving lines of equal strenght or several lines covering a range of opacities which are weighted to simulate a distribution of line strengths. We find acceleration near the base of the wind which is considerably more gradual than in the model of Castor, Abbott, and Klein. This difference is significant even well above the point. In our model, v(r) is approximately linear out to 1.3--1.4 stellar radii, where the velocity reaches one fourth the terminal velocity. Observations also support slower acceleration in this region. The mass-loss rate and the wind structure at large radii are in substantial agreement with earlier results. The mass-loss rate is NL/c/sup 2/, where N is the number of lines which contribute significantly to the radiation pressure force. For a reasonable line strength distribution, the terminal velocity is several timesmore » the escape velocity.« less