The paper presents a matrix method of analysis of prismatic shells with a box-type cross-section with two axes of symmetry. Such a prismatic shell is approximated by a suitable design model allowing for the warping and distortion of the cross section. The problem is solved using Vlasov's variational method in conjunction with the transfer matrices. The procedure is illustrated by two examples, one of which indicates that the diaphragms stiffening the cross-section may not be beneficial in a global sense.