Model Driven Engineering (MDE) is a state-of-the-art software engineering approach, which adopts models as first class artefacts. In MDE, modelling tools and task-specific model management languages are used to reason about the system under development and to (automatically) produce software artefacts such as working code and documentation. Existing tools which provide state-of-the-art model management languages exhibit the lack of support for automatic static analysis for error detection (especially when models defined in various modelling technologies are involved within a multi-step MDE development process) and for performance optimisation (especially when very large models are involved in model management operations). This thesis investigates the hypothesis that static analysis of model management programs in the context of MDE can help with the detection of potential runtime errors and can be also used to achieve automated performance optimisation of such programs. To assess the validity of this hypothesis, a static analysis framework for the Epsilon family of model management languages is designed and implemented. The static analysis framework is evaluated in terms of its support for analysis of task-specific model management programs involving models defined in different modelling technologies, and its ability to improve the performance of model management programs operating on large models.