The deformation of the elastic transverse isotropic layer under normal pressure applied on the outer and inner surfaces is analyzed. For the shell, which is much softer in the transverse direction than in the tangential plane, one gets singularly perturbed boundary value problem. Solution of the problem in zero approximation allows to obtain the asymptotic formula for the change of the relative layer thickness under normal pressure. The asymptotic results well agree with the exact solution. Refs 5. Figs 3.