Buckling capacities of rigid frames with nonuniform members are analyzed by a numerical method using divided segments. Fundamental and higher buckling loads and modes result from the eigenvalues and eigenvectors of a matrix which is the product of a sidesway flexibility and a second-order stiffness matrix. The sidesway flexibility matrix is obtained directly from the shape of the rigid frame and the elastic properties of the segments. The second-order stiffness matrix is defined by the axial forces in the segments. The method is approximate in that the flexural stiffness coefficients of the segments are those for uniform sections and without axial forces. A computer and numerical examples are provided.