Software testing is widely recognised to be an expensive, error prone and time consuming process and this has led to much interest in automated test generation. In recent years, search based techniques such as Genetic Algorithms have been applied to a range of test automation problems but much of this work has concerned white-box testing. This talk will provide an overview of recent progress in Search Based Software Testing (SBST) in the context of model based testing. Specifically, it will review work on the use of SBST methods in testing from finite state machines and extended finite state machines.