Abstarct: In this research, the mathematical solution of the governing equations of a thin axially moving viscoelastic web under lateral pressure has been investigated. The web translates axially with a constant velocity between two pairs of rollers and it is subjected to a uniform tension at the both ends. The equations of motions, which are a system of partial differential equation, have been derived by using the Hamilton’s principle. The behavior of the viscoelastic web has been defined with a three-parameter Zener model in shear and elastic in bulk. The matched asymptotic expansion method (MAE) and Laplace transform has been applied to obtain the displacements in Laplace domain. These displacements have been transmitted to the time domain by using residual theorem. baxsed on this analytical solution, the composite solution of the system, the critical speeds and the natural frequencies, were determined for a given set of initial values. Finally, a parametric study has been performed to investigate the effects of various parameters such as thickness, viscoelastic properties, density and translating speed on the system response.