This paper demonstrates how procedural modeling and computer graphics techniques can be combined for creating fast, accurate and realistic modeling of archaeological parts of buildings which can be used for games and virtual environments. As a case study the Ionic order of Greek and Roman temples is examined. In particular, the temple of Portunus in Rome, Italy was used as a case study. A set of geometric algorithms for computing shape points based on curved surfaces are presented, which allows creating the majority of Ionic temples. Evaluation of the results is performed based on the Hausdorff and Frechet distances and results indicate that the proposed method provides a very good approximation for generating accurate Ionic order temples. However, ornaments that usually decorate the column capital have not been taken into account in this paper.