Positive displacement expanders are quickly gaining popularity in the flelds of micropower generation and refrigeration engineering. Unlike turbomachine s, expanders can handle two-phase flow applications at low speed and flow rate levels. This paper is concemed with a simple-design positive displacement expander based on the limaçon of Pascal. The paper offers an insight into the thermodynamic workings of the limaçon gas expander and presents a mathematical model to describe the manner in which the port locations affect the expander performance. A stochastic optimization technique is adopted to flnd the locations, for the expander ports, which produce best expander performance for given chamber dimensions. The operating speed and other parameters will be held constant during the optimization procedure. A case study is offered in this paper to prove the validity of the presented approach, and comments are given on how various operating parameters affect system performance in the limaçon design.., '