This paper presents a finite-difference approach for analysing prismatic shells of varible cross-section. Such shells have wide application in machine tools and mechanical handing. The construction of the design model allows for warping and distortion. The problem is formulated by use of Vlasv’s variational method and solved by means of a finite-difference technique for various boundary conditions. The results are compared with those obtained by use of the cylindrical-shell theory developed by Krishanamurthy and the theoretical and experimental results obtained by Kristek. A study of the influence of various geometric parameters such as thickness of shell, length of shell, taper angle, and number of diaphragms is also made. © 1975, Institution of Mechanical Engineers. All rights reserved.