The problem on the stress-strain state (SSS) of thick-walled shells of revolution bounded by surfaces with the small amplitude of departure from spherical ones is solved with allowance for the first three approximations. With this in mind the general solution of equilibrium equations for a transversal-isotropic medium in a spherical coordinate system within the framework of the second variant of the boundary perturbation method (BPM) has been used. Based on the analytical solutions and numerical data obtained, the stress-strain state of the shells subject to constant or variable axisymmetric (internal and external) pressure is analyzed. The influence of the geometric parameters of equations for noncanonical surfaces with various shell shapes on the redistribution of stresses in comparison with a spherical shell (canonical shell and zero approximation) is demonstrated. Parametric representation of the equations of noncanonical surfaces and, respectively, differential operators in approximations made it possible to calculate within the framework of a single algorithm the stress-strain state of a number of shells with various configurations. The stress concentration numerical data at characteristic points (minimum thickness under maximum loading) of the shell are obtained. It is shown how variation in the curvature of the shell surface affects the magnitude and nonlinear character of stress distributions, which are consistent with asymptotical properties of solutions under the oscillating law of variations in boundary conditions. Particularly, the shells with oscillated surfaces are associated with equilibrium equations (as the systems of partial differential equations) with Lame’s coefficients dependent on rapidly varying functions that appear in equations of boundary surfaces. The asymptotic solution properties of such systems of differential equations have been studied by M.I. Vyshik and L.A. Lyusternak.