One reason that human interaction with technology is difficult to understand is because the way in which people perform in- teractive tasks is highly adaptive. One such interactive task is menu search. In the current article we test the hypothesis that menu search is rationally adapted to (1) the ecological struc- ture of interaction, (2) cognitive and perceptual limits, and (3) the goal to maximise the trade-off between speed and ac- curacy. Unlike in previous models, no assumptions are made about the strategies available to or adopted by users, rather the menu search problem is specified as a reinforcement learning problem and behaviour emerges by finding the optimal pol- icy. The model is tested against existing empirical findings concerning the effect of menu organisation and menu length. The model predicts the effect of these variables on task com- pletion time and eye movements. The discussion considers the pros and cons of the modelling approach relative to other well-known modelling approaches.