A recently developed theoretical approximation, the Reflected Afterflow Virtual Source (RAVS) model, is applied to the case of a planar shock wave attacking an elastic cylindrical shell. To do this, an equation of motion for a structural surface is presented. Also, equations for the pressure that develops when an acoustic wave interacts with a curved and compliant surface are presented. These equations were derived using the RAVS model. An expression for the velocity of the structural surface is derived from the equation of motion and a numerical method is developed using this expression. This is applied to the case of a planar wave attacking an elastic cylindrical shell. Calculations, using the RAVS model, are shown to be in good agreement with all of the exact calculations that were published by Huang for all locations and times. It is concluded that the RAVS model gives a good approximation for the loading and response of an elastic cylindrical shell attacked by a planar wave. The RAVS model is shown to be even better for a spherical wave attack which is a case of more practical interest.