Computer game technology is increasingly more complex and applied in a wide variety of domains, beyond entertainment, such as training and educational scenarios. Testing games is a difficult task requiring a lot of manual effort since the interaction space in the game is very fine grained and requires a certain level of intelligence that cannot be easily automated. This makes testing a costly activity in the overall development of games. This paper presents a model-based formulation of game play testing in such a way that search-based testing can be applied to generate tests automatically. An abstraction of the desired game behaviour is captured in an extended finite state machine (EFSM) and search-based algorithms are used to derive abstract tests from the model, which are then concretised into action sequences that are executed on the game under test. The approach is implemented in a prototype tool EvoMBT. We carried out experiments on a 3D game to assess the suitability of the approach in general, and search-based test generation in particular. We applied 5 search algorithms for test generation on three different models of the game. Results show that search algorithms are able to achieve reasonable coverage on models: between 75% and 100% for the small and medium sized models, and between 29% and 56% for the bigger model. On the actual game application, tests kill between 34% and 99% of mutants and reveal two previously unknown faults.