This paper describes a methodology to evaluate the elastic shear buckling strength of H-shaped members under shear force. The methodology is based on energy method applying novel displacement functions which are able to capture shear buckling deflections for various cross-sectional profiles of H-shaped sections by using unique trigonometric series. With the proposed displacement functions, a high-precision equation, which can predict the shear buckling strength, can be obtained. To clarify the accuracy of the equation, a parametric eigenvalue analysis based on the finite element method is performed.