Crowdshipping (CS) is an emerging form of freight transport that is expected to reduce the externalities of urban freight transport. The supply of CS services originates from people with an intention to travel, who can choose to engage in a parcel delivery service as incidental carrier. The popular expectation is that this consolidation of freight and passenger trips could save freight trips and thus alleviate urban transport congestion and environmental pollution. A key challenge in the prediction of CS service volumes and impacts, however, is to match existing service demand and supply. This has not yet been addressed in the literature with models that give an empirically realistic representation of individual decision-making. We approach this problem using a disaggregate activity-based models for urban passenger transport and freight transport. Allocation of parcels to travellers is done based on a simulated random utility discrete choice model. We present a first case study for the city of The Hague, The Netherlands, to illustrate empirically the model. Our findings suggest that CS could result in increased CO2 emissions and total vehicle distances travelled.