A simplified computer-based structural analysis procedure has been developed for evaluating the stresses in a lower limb prosthetic socket when subjected to external loads. This technique has been tested by studying a simple linear axisymmetric shell subjected to uniform loads. It was found that the stress and strain distributions obtained are close to those determined by a finite element technique. The method that has been proposed involves an incremental procedure, which can be used to analyse the behaviour of a prosthetic socket of irregular shape made from non-linear anisotropic materials. By employing the proposed procedure to study an example, in which a simplified lower limb prosthetic socket is subject to internal pressure and frictional forces, the effects of the material non-linearity have been found to be significant.