The current deals with the determination of the 'true' geometrical shape of the Great theatre of Ephesus, which is the largest theatre in Asia Minor. To detect the geometrical form of the theatre a precise point dataset was created using terrestrial measurements performed directly on the theatre site. The well-known ellipse and circle fitting algorithms were presented for detecting the precise geometrical shape of the amphitheatre rings. The study reveals that ellipse geometry fits well to the theatre arcs that is amphitheatre rings are generally elliptical in shape. The precise metric values of the parameters of the geometrical shape were computed to characterise theatre features.