The interpretation of localized density structures in the high-latitude ionosphere as observed by ground ionosondes is a task that is complicated by the complexity of those structures and by the variety of processes that ionosonde waves undergo. To aid interpretation, we have performed a first-order analysis of the shapes of traces seen in ionosonde displays. This has been done using an idealized model of a particular structure of current interest, a polar ionospheric patch. The patch is modeled as a spheroidal enhancement of density superposed on a horizontally stratified F layer. Ray tracing is used to find O- and X-mode rays that reflect back to a ground ionosonde after total reflection. Theoretical curves are calculated for swept-frequency (h'ƒ), fixed-frequency (h't), and Doppler-frequency (ƒDt) operational modes. The computed h'ƒ curves have U shapes, the h't curves are quasi-hyperbolic, and the Doppler curves have reverse-S shapes. By moving the patch through a series of horizontal separations from the ionosonde, the sequence of curves is calculated for a patch passing by an ionosonde. The theoretical traces have been compared with data from the Canadian advanced digital ionosondes (CADIs) at Resolute Bay, Eureka, and Alert. The CADI h'ƒ traces are observed usually to have incomplete U shapes, missing their lower-frequency arms. In the light of the ray tracing the CADI results are consistent with the hypothesis that HF-scattering irregularities are found on both the leading and trailing edges of patches but are stronger on the trailing edge. Similar results have been reported for scintillation-causing irregularities. This points to the dominance of the gradient-drift instability. The hyperbolic h't curves are asymmetric, having slower downsweeps than upsweeps. This can be caused by horizontal asymmetries in the patch density distribution. Often, polar patches seen by CADI are not single, isolated enhancements. Rather, they appear as composites of substructures, each of which mimics certain aspects of the single patch described by the present theoretical model.