We derive an Airy stress function solution for a submarine or subareal, infinite or finite, elastic wedge with a frictional basal fault. The solution has a simple compact expression and has corrected errors present in earlier elastic wedge solutions. We use the solution to study frequently observed bending-like behavior of relatively thin wedges, in which lateral tension and compression coexist but are vertically partitioned. Conditions to cause such coexistence are best understood by examining how the position of a neutral line changes in response to variations in basal traction, pore fluid pressure, and wedge geometry. We have used the example of the Mauna Loa--Kilauea rift flank in Hawaii to illustrate how the solution may be applied to geological problems. Our results generally support the concept of a "bent" elastic wedge previously proposed to explain coeval normal faulting in the upper part and reverse faulting in the lower part of the rift flank. However, we find that coexistence of tension and compression in a wedge of this type can occur over a much wider range of pore fluid pressure values and basal friction conditions than previously thought and does not require unusual geological processes.