Dynamical equations describing the amplification and propagation of an initial Stokes seed pulse in a synchronously pumped fiber Raman laser configuration are formulated and analytic solutions are derived. A train of Stokes shifted pulses are produced, whose individual characteristics eventually evolve on successive round-trips through the fiber into subpicosecond pulses having constant fluence and decreasing temporal duration. Raman pulse compression stops when it is counterbalanced by the effects of group velocity dispersion and phase modulation in the normal dispersion regime. Pulse breakup due to soliton formation can occur in the anomalous dispersion regime. Simple expressions for the rate of pulse compression, steady-state pulse fluence, and for the minimum steady-state pulse duration are obtained.