The authors consider the heating, by magnetic pumping, of a radially non-uniform plasma cylinder of non-uni form radius located in a longitudinal, constant and uniform magnetic field B. An oscillating magnetic field having the form of a travelling wave with phase velocity ω/k of the order of the ionic thermal velocity is produced by means of external azimuthal electric currents. The frequency of the oscillating field ω is significantly less than the reciprocal of the ion-ion collision time 1/τi, and the ion cyclotron frequency ωi, the plasma electrons are magnetized (the electron cyclotron frequency is considerably greater than the reciprocal of the electron-electron collision time), and the plasma pressure is significantly less than the magnetic pressure.Simple expressions are obtained for the energy absorbed per unit time by the plasma as a result of dissipative effects: ion viscosity and longitudinal electronic heat conduction (Joule losses play a minor role in magnetic pumping). Particular attention is paid to the case of acoustic resonance, where the inhomogeneous plasma contains a layer in which the velocity of sound is equal to the phase velocity of the excited wave. In this situation the absorption of energy by the plasma increases sharply and the increase in plasma temperature T is determined to within an order of magnitude by the relation dT/dt ∼ ωT(B∼/B)2, where B∼ is the amplitude of the oscillating magnetic field at the axis.