In this paper we propose an assignment model on urban networks to simulate parking choices; this model is able to simulate the impact of cruising for parking on traffic congestion. For simulating parking choice and estimating the impact of cruising on road congestion we propose a multilayer network supply model, where each layer simulates a trip phase (on-car trip between the origin and destination zone, cruising for parking at destination zone and walking egress trip). In this model the cruising time is explicitly simulated on the network. The proposed model is tested on a trial network and on a real-scale network; numerical tests highlighted that the proposed model is able to simulate user parking choice behaviour and the impact of cruisi...