In this paper, stability analysis of continuously restrained Euler columns of variable flexural stiffness is conducted by using homotopy perturbation method (HPM). The restraint considered in this study is an elastic foundation model in engineering practice and it is of great interest to foundation engineers. Critical buckling loads are investigated considering different end conditions. Obtaining analytical solutions for these types of problems was very difficult, now the condition is changed. The study proves that HPM is a very efficient and promising approach to the elastic stability analysis of specified problems.