The article discusses the buckling analysis of composite orthotropic truncated conical shells under a combined axial compression and external pressure and resting on a Pasternak foundation. The governing equations have been obtained for the orthotropic truncated conical shell resting on a Pasternak foundation and solved by applying the Superposition and Galerkin methods. The novelty of present work is to achieve closed-form solutions for critical combined loads. Finally, the effects of the Winkler and Pasternak elastic foundations, shell characteristics and material orthotropy on the values of critical combined loads have been studied. Comparison of results with those available in the literature has been presented. (c) 2014 Elsevier Ltd. All rights reserved.