The calculation of flexural buckling loads for structural members remains a relevant topic of practical and theoretical interest. In addition to well-known solutions for prismatic members, solutions are available for the buckling loads of nonprismatic and weakened members; however, these solutions are often specialized and difficult to implement, as are finite element analyses that require a refined mesh in order to achieve accurate solutions. A straightforward approach for computing buckling loads based on eigenvalue analysis of the curvature-based displacement interpolation (CBDI) influence matrix is developed. The CBDI influence matrix, which is a byproduct of a force-based frame element formulation of geometric nonlinearity, simplifies the calculation of flexural buckling loads for nonprismatic and weakened members while also providing accurate results for prismatic members. Comparisons with previously published solutions show the CBDI approach gives accurate first-mode buckling loads for prismatic and nonprismatic columns when the CBDI influence matrix is formed using at least three interpolation points. More interpolation points are required for the critical buckling loads of columns where the change in flexural stiffness is more abrupt. The CBDI approach is easy to implement and provides engineers and researchers a means of calculating flexural buckling loads for members with arbitrary changes in flexural stiffness.