In this paper, the authors theoretically analyzed the strength of a specially shaped vessel having an elliptical cross section and a finite shell length. At the first step, taking the cross section to be a quasi- ellipse formed by the arcs of two circles, and assuming a considerably simple mathematical expression based on the experimental results, the theoretical formula was derived by means of the strain-energy method. In the second place, comparing the theoretical values with those experimentally obtained, it has been confirmed that the formula is very sufficient, unless the shell length is extremely long, in coincidence with the actual stresses and deformations at the central portion of the shell where the effect of the length is supposed to be very dominant. Moreover, using the above formula, the authors were able to theoretically prove the characteristic phenomenon that the longitudinal stresses are higher than the circumferential stresses in case of a short length shell.