Abstract In an earlier paper (1) 2 by the author the theory of axially symmetrical shells was extended to include the body force of rotation about the axis of generation, and the results were applied to the conical shell. In the present paper this theory is used to obtain the solution for a bell-shaped rotating shell whose middle surface is generated by revolving a circular arc about a tangent line. The defining relation is an ordinary linear differential equation of fourth order with variable coefficients. A differential analyzer solution was used and this involved the problem of handling boundary conditions which were divided between both extremities of the range of the independent variable. Comparisons of the results with those of the conical shell and with the membrane theory are made.