The large-deflection analysis and postbuckling behavior of laterally braced or unbraced slender beam columns of symmetrical cross section subjected to end loads (forces and moments) with both ends partially restrained against rotation including the effects of out-of-plumbness is developed in a classical manner. The classical theory of the “Elastica” and the corresponding elliptical functions utilized herein are those presented previously by the senior writer. The proposed method can be used in the large-deflection elastic analysis and postbuckling behavior of slender beam columns with rigid, semirigid, and simple flexural connections and both ends. Only bending strains are considered, i.e., the effects of axial and shear strains are neglected. An example is included that shows the effects of flexible connections at both ends on the large-deflection analysis and postbuckling behavior of slender beam columns.