Deflections and stresses are analyzed for a noncircular cylindrical shell of uniform wall thickness under hydrostatic load and with its edges clamped in such a fashion that the end sections remain plane and normal to the axis. By assuming a Fourier series in the closed circumferential direction and using the principle of the minimum of the total potential, the partial differential equations of equili rium are replaced by a set of ordinary differential equa ions. The displacements obtained by solving these equations are used to obtain the stresses. The results are then compared with those obtained by 2 simple approximate solutions for circular cylindrical shells. Numerical results are obtained for an oval shell with a circumference-to-wall thickness ratio of 576, a circumference-to-axial length ratio of 24, and a major-to-minor axis ratio of 1.10. The maximum radial displacement occurs at points on the shell determined by the intersection of the midlength cross section with the generators representing the loci of least curvature. The maximum stress is an axial stress due principally to bending, and occurs at those points of the clamped edges having the least curvature.