This paper considers a pursuit-evasion game for non-holonomic systems where a group of pursuers attempts to capture an evader in a bounded connected domain. The problem is challenging because all vehicles have the same maneuvering capability in terms of speed and turn radius constraint. The paper initially discusses a simple approach for holonomic systems that is based on the minimization of the safe-reachable area (the area containing the set of points to where an evader can travel without being caught). This idea is then extended to develop a pursuit-evasion strategy for non-holonomic systems. However, solving such a problem is computationally intractable. Therefore, we propose a computationally efficient algorithm to obtain approximate solutions. This paper also proposes an alternative approach to obtain a simple yet effective solution to the cooperative pursuit problem that is based on missile guidance laws. As there is no analytical proof of capture, we empirically evaluate the performance of the algorithms and perform a comparative study using solutions obtained from umpteen simulations. A total of four different cooperative pursuit strategies and three different evader strategies are taken into account for the comparative study. In the process, an evader strategy which is superior to that based on the optimization of safe-reachable area is also identified. © 2016, Springer Science+Business Media Dordrecht.