Abstract: This paper presents a step-by-step approximating method to obtain the analytical solutions of the differential equations for the self-similar problems of viscous fluid flow (1. 1-1. 4). Prosnak (1969) obtained solutions of these equations by using a small parameter method, but he reduced the governing equations to the linear differential equations with constant coefficients.

Key words: structural stability, buckling, postbuckling, cylindrical panel, higher order shear deformable shell theory, boundary layer theory of shell buckling, singular perturbation technique