At launch, coronal mass ejections (CMEs) are often approximated as locally cylindrical objects with circular cross sections. However, CMEs have long been known to propagate almost radially away from the Sun along with the bulk solar wind. This has important consequences for the structure of CMEs; an initially circular cross section will be severely flattened by this radial motion. Yet calculations of total flux and helicity transport by CMEs based on in situ observations still use the assumption of a locally cylindrical object. In this paper, we investigate the morphology of an interplanetary CME based upon geometric arguments. By radially propagating an initial cylindrical object that maintains a constant ratio between its expansion speed and bulk flow, A, we show that the flattening, or "pancaking," of the two-dimensional cross section effectively ceases; the aspect ratios of these CMEs converge to a fixed value as they propagate further into the heliosphere. Thereafter the CME morphology is scale invariant. We predict aspect ratios of 5 ± 1 at terrestrial distances. By correlating a planetary shock with an interplanetary shock linked to a CME, these aspect ratios are estimated using in situ measurements in Paper II. These estimates are made at various heliocentric distances.