The authors use a nine-noded degenerate solid shell element as the basis of a finite element analysis, with automatic adaptive refinement, of shell structures. In order to avoid locking, an assumed strain formulation is built into the element. The error in finite element solutions is estimated by the Zienkiewicz-Zhu error estimator, and the stress used in the error estimator is a smooth field which is recovered with the aid of a patch convective coordinate system. Of particular interest is the ability of the method to overcome difficulties associated with singularities and boundary layers. A range of examples is presented: the effect of singularities, and the performance of the adaptive procedure. As expected, it is found that the degenerate solid element is better able to predict the presence of boundary layers than flat facet elements. Furthermore, the adaptive scheme is seen to reduce or eliminate the effects of singularities. Finally, the stress recovery procedure appears to lead to reliable stress fields, though these were not compared with closed-form solutions.