Earlier work demonstrated that the characteristic resonant frequency of magnetoelastic thick-film sensors shifts linearly downwards in response to increasing atmospheric pressure. In this paper, the response mechanism is detailed and shown to be a function of both pressure and the way that the sensor is mechanically stressed. Stressing the sensor, in either the elastic or plastic regime, induces out-of-plane vibrations that act as a pressure-dependent damping force to the longitudinal sensor oscillations excited by the interrogation field. This damping force, in turn, acts to shift the resonant frequency of the magnetoelastic sensor lower in response to increasing pressure.