"The form of a brachiopod shell is the product of the rates of growth operating at all points on the valve edges during successive stages of growth. Shell form is analysed here in terms of these rates of growth, the rate at each point being resolved into component rates. If the antero-posterior growth gradients are linear, the shell is rectimarginate; if non-linear, the lateral commissure is 'flexed' throughout ontogeny. Localized anomalies in the growth rate may modify either of these basic growth patterns at any stage in ontogeny. They produce deflections in the commissure, and these generally produce deformations in the valve surfaces (e.g. folds, sulci, costae). Two major varieties of external hinge structure are defined: strophic shells have a true hinge line and may also have interareas; non-strophic shells have no true hinge line but may have palintropes. The implications of this formal analysis are examined in relation to the systematic description of the shell form."