Abstract <p>The study presents derivation of asymptotic equations describing the elliptic boundary layer in shells of revolution under normal impact surface loading. The considered boundary layer type occurs only under surface and edge impact loading and is localized in the small neighborhood of the conditional front of Rayleigh surface waves. The study uses asymptotic methods in combination with A.I. Lure’s symbolic method. Elliptic equations describing the behavior of the boundary layer along the shell thickness and hyperbolic equations defining the boundary conditions on the shell faces are derived. </p>