The Airy stress function is used, via the Principle of Superposition and the series summation concept, to obtain stress states in a static, self-gravitating elastic beam subjected to boundary stresses. The boundary conditions investigated are more complicated than those previously published and include cases with sawtooth-, step-, and sinusoidally-shaped lower boundary loads, with and without additional tectonic end loads. Potential shear fracture (fault) patterns derived from the calculated stress fields indicate co-existing (simultaneous) regions of lateral shortening and extension. Application of three of the cases to the study of the structural geometry of the Wind River, Owl Creek, and Beartooth Mountains of Wyoming yields a good "fit." For the case of the upthrust structures, these solution provide a possible explanation for the observed rotations and zones of shortening and extension.