This study aims to determine the critical buckling load of tapered members under axial force by modifying a well-known equation called the Euler Equation. The mathematical model derived in this research is based on special functions called stability functions. However, the elastic critical load of non-prismatic members is analyzed using the modified slope deflection equations. In this study, the developed equation is named the Modified Euler Equation as an extension of the Leonhard Euler equation that introduced in 1757. One of the primary assumptions of the proposed equation is considering the effective member length as the length between member ends at pinned–pinned boundary conditions. The member under consideration is assumed to be a linearly tapered member while the other model assumptions are the same of the Euler formula assumptions used for prismatic members. The modified Euler load equation for non-prismatic members is evaluated using finite element method. The results presented in this research showed that tapered columns have significantly more elastic capacity than a prismatic member that has an equivalent geometry.