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Post-buckling and collapse phenomenon of a thick closed ring subjected to external pressure on its outer surface is analyzed in this research. Ring is made of a linearly elastic polar orthotropic material. Constitutive law of linear elasticity under plane stress conditions is used. Virtual work principle is implemented to obtain the governing equations. Unlike the available noncompressible ring theories, a two-dimensional elasticity solution including the complete nonlinear Green strain field is used. The finite element method is used to solve the highly nonlinear coupled equilibrium equations. The well-known Newton-Raphson iterative technique is applied to the matrix representation of the equilibrium equations to trace the post-buckling response of the ring up to the collapse point where two antipodal points on the interior side of the ring are collided with each other. It is shown that, including the complete Green strain field is necessary in accurate estimation of the post-buckling path, especially for higher load levels and collapse load. Furthermore, orthotropic rings under external pressure load follow the bifurcation type of buckling accompanied with a stable post-buckling path. [ABSTRACT FROM AUTHOR]