The purpose of this research is to drive the evaluation formula of coupled local buckling strength of H-shaped members under pure compression. To clarify the interaction among plate elements, multiple studies have been conducted. As a result, the evaluation formulae for maximum strength are established and expressed by empirical equations or regression analysis equations . However, most equations were not able to explain the local buckling behavior of H-shaped members because the local buckling behavior is complicated. To solve this problem, Prof. Ikarashi proposed a displacement function using a Fourier series to drive an evaluation formula based on the energy method. By using the Fourier series, the buckling deflection can be described even if combined stresses act on H-shaped members. In this paper, the evaluation formula is proposed based on the energy method, as well as Prof. Ikarashi did. The difference between Prof. Ikarashi’s researches and this research is the displacement function. The exponentiation of the trigonometric function is used as a particular buckling displacement function. Because the function is fast-converging compared to the Fourier function, it is possible that the buckling deflection can be described by only three terms. Additionally, the function can describe elastic web-flange interaction amongst the elements comprising the cross section. As a result, the closed-form evaluation formula of H-shaped members is proposed. To verify the reliability and the effectiveness of the proposed formula, modal analysis based on the finite element method (FEM) is conducted.