A hollow cylinder is encased in a thin elastic shell and subjected to a time harmonic pressure at the inner surface of the cylinder. Plane strain and axial symmetry are assumed. The material of the cylinder is incompressible in bulk and both elastic and viscoelastic behavior in shear are considered. The inner radius of the cylinder increases monotonically with time. The influence of loss of mass and stiffness on the forced motion of the system is considered. The oscillatory motion consists of the superposition of a maintained vibration and a transient term. The maintained vibration takes into account the loss of mass and stiffness in a quasistatic manner. For an encased viscoelastic cylinder, the transient term is damped rapidly. A bounded resonance effect occurs when the instantaneous frequency of the system passes through the value of the external forcing frequency.