Buckling analysis of column as the primary structural member has a special place in engineering research. Because of increasing stability and reducing structural weight and consequently reducing earthquake forces, the use of non-prismatic columns in frames have increased recently. The most important issue in the stability of column is to determine the critical buckling force. For this purpose, the stability differential equation should be solved. In many studies, the solution of differential equation using analytical methods are not possible.
 In this regard, researchers use numerical methods for solving the governing equilibrium equation and determine buckling load, respectively. Power series method is one of the most powerful and advanced numerical methods for solving linear differential equations with variable coefficients which has many applications in science and engineering. In this study, columns’ cross-sections change by power functions and or exponential ones. Exponential variation is one of the most special states of non-prismatic columns that lees methods are able to solve its governing differential equation. Therefore, the stability differential equations governing the non-prismatic columns with different boundary conditions solved by using power series expansion and considering the flexural rigidity changes as a McLaurin expansion. The elastic critical buckling load calculated by solving eigenvalues. The results of numerical examples solved with this method compared with the results of other methods, indicates that the power series methods as one of the most powerful methods for solving complex differential equations,  has sufficiently accurate and high speed  in stability analysis of elastic columns with variable cross sections.