We present the MOdel of Organisational Change using Agents (MOCHA) as a means to formally specify, check and simulate organisations and their changes using agents. We define the structure of the organisation without making any assumptions about the internal characteristics of the agents who will populate it. We adopt a normative view of organisations, and capture a notion of social influence through relationships between roles. Ours is a flexible and expressive approach that contemplates agents taking part in multiple organisations with distinct roles and disparate (possibly conflicting) obligations. We make a distinction between the structure of an organisation and the population instantiating the organisation, and our framework allows the consequences of change in both the organisational structure and the population to be investigated. We also describe a machine-processable representation of our model and show how it can be used to support engineering activities.