I describe a mathematical model of shells that incorporates simple morphometric measurements, which can be obtained easily from sectioned specimens. The model reconstructs form (size and shape) by describing the path in space traversed by, and the changes in dimensions of, a shell aperture during accretionary growth. The model contains parameters that independently affect components of these two aspects of shell form in directions radially away from (or toward) and along a coiling axis. I also describe a computer program, CerioShell, that uses the mathematical model to graphically simulate shell forms. The program permits the viewing of images from different three-dimensional orientations, using various graphical representations, and provides dimensions of the images it generates. Together, the model and the program allow one to investigate the effects that changes in modes of growth would have on shell form.