Among the shells of invertebrates that exhibit spiral growth, differences in form can be expressed by differences in geometric parameters. If three of these parameters are considered at a time, the spectrum of possible shell forms may be shown by a block diagram. Analog and digital computer constructions make it possible to visualize shell forms that are theoretically possible but do not occur in nature. Actual species are not randomly distributed in the total spectrum of theoretically possible forms. Functional and evolutionary groups are confined to discrete regions of the spectum. Rational explanations for several of the observed distributions are apparent and may be expressed in terms of shell function. For example, a bivalve must have non-overlapping whorls in order to have a functional hinge. This fact restricts the geometric range of both brachiopods and bivalved molluscs. Ontogenetic change in coiling geometry may be interpreted as a compensation for the effects of increase in absolute size during growth.