REST (REpresentational State Transfer), relying on resources as its architectural unit, is currently a popular architectural choice for building Web-based applications. It is shown that design patterns—good solutions to recurring design problems—improve the design quality and facilitate maintenance and evolution of software systems. Antipatterns, on the other hand, are poor and counter-productive solutions. Therefore, the detection of REST (anti)patterns is essential for improving the maintenance and evolution of RESTful systems. Until now, however, no approach has been proposed. In this paper, we propose SODA-R (Service Oriented Detection for Antipatterns in REST), a heuristics-based approach to detect (anti)patterns in RESTful systems. We define detection heuristics for eight REST antipatterns and five patterns, and perform their detection on a set of 12 widely-used REST APIs including BestBuy, Facebook, and DropBox. The results show that SODA-R can perform the detection of REST (anti)patterns with high accuracy. We also found that Twitter and DropBox are not well-designed, i.e., contain more antipatterns. In contrast, Facebook and BestBuy are well-designed, i.e., contain more patterns and less antipatterns.