This work addresses the issue of fitting a geometrical shape to the Hierapolis theater near the city of Denizli, Turkey. The aim of the study was to determine the geometrical shape of the theater that would best fit the set of measured site data points. The geometrical form of the theater was surveyed by using an electronic total station instrument. Because theater rings are generally elliptical in shape, the well-known ellipse-fitting algorithm was presented for computing the geometrical parameters. In this study, the authors plan to analyze the fitting algorithm presented, determine the best-fitting geometrical shape (e.g., an ellipse, a circle) to the Hierapolis theater, and characterize its features. Because the fitting accuracies are not sufficient to decide which geometrical shape is appropriate, a statistical testing procedure was applied to identify statistical differences between the related geometries. The most probable geometrical shapes for this purpose were determined with the use of the statistical equivalence test. (C) 2014 American Society of Civil Engineers.