There are numerous examples in the aero and power producing industries of components which are designed to sustain creep deformation. An important class of structures in this category lies in pressurised shells of revolution. The few analyses which allow predictions of creep deformations to be made are usually restricted to the secondary creep problem, contain approximate relations between stress resultants and deformations or ignore the important effects of bending. While the neglect ot primary creep is not important for cases of steady loading sustained for long periods, stress redistribution should be calculated if the loading period is less than the time taken to reach a stationary state of stress; such a state of affairs is very likely in two-shift operated power producing plant and also in aircraft components. Approximations involving concepts of “sandwich” shells that are often made to form moment-curvature rate relations can be dispensed with by integrating the stress-strain rate relations through the shell thickness. Although the stresses become non-linear through the shell wall they are slowly varying and the integration introduces no problem. The integration requires the use of a digital computer but creep problems have to be solved numerically, except in a very few cases, so that whatever the assumptions automatic computation is necessary. While some practical shells approximate to the momentless condition the most likely case will include bending which, although likely to be relaxed by a process of stress redistribution, will cause additional creep straining.