The magnetic response of a type II superconductor to an applied magnetic field is described by solving the Bean model and viscous flux flow equations simultaneously. Two analytical solutions are presented, which detail the flux distribution within the superconductor induced by a sawtooth-like applied magnetic field. The resultant hysteresis loops show features which depend strongly on the 'sharpness' of the sawtooth waveform. As expected the magnetic hysteresis losses increase with frequency, reflecting the viscous nature of the flux flow. In the zero frequency limit, as the velocity of flux flow approaches zero, the usual Bean result is obtained.