By using a comprehensive rotating laminated shell model of the tire, the effects of viscoelastic damping on the standing wave phenomenon are investigated in more detail than was previously possible. The shell theory employed is a nonlinear version of Novoshilov's work and the onset of the standing wave is characterized as a small dynamic deformation superposed on a finite deformation. To expand the scope of the model, the viscoelastic constitutive law is treated as either of the differential or hereditary integral type. The solution for the stated model is obtained by the finite element procedure, and the results of several numerical experiments are presented. The substantial role of viscoelastic effects in the development of the standing wave phenomenon of tires is emphasized by the results.