This paper, the third of a series, presents the results of computations for determining the stresses in a pressure vessel with a hemispherical head. The bending theory of shells is used to evaluate the maximum stress at the junction between head and shell. Tables show the magnitudes of the shear stress, the axial stress, and the circumferential stress at the junction as multiples of pd/2t. The axial and circumferential stress have been computed for both surfaces. Additional results show the magnitude, sense, and location of the maximum stress (of each of the three types) in the shell. The largest value of the diameter-thickness ratio of the head for which computations were made is 40. When the diameter-thickness ratio of the head exceeds 40, well-known approximate theories can be used. The limit of 40 is imposed by the slow convergence of the hypergeometric series. Tables of influence numbers for both the head and shell are included for application to other problems. A brief discussion of the mathematical procedure is included.