This paper centres on the development of a geometrical representation of movement and spatial interaction in urban areas, as distinct from the network representation commonly used in modern studies. All quantities are treated as distributions over geographic space, rather than concentrations at nodes of a network. We present a continuous model of spatial interaction and calibrate it for Greater Manchester. The model is a trip distribution model which produces an allocation of trips from any area to all other areas in accordance with a derived trip density function. The inputs to the model are density functions for residences and workplaces of car commuters, and a velocity field. The velocity field defines a measure of the travel time between different locations. The outputs of the model are spatial distributions of accessibility of locations to jobs and residences, and a spatial distribution of traffic flow. We find that the location most accessible to jobs in Manchester is not in the centre of the city, but in a ring more than half a mile away from the centre. The maximum accessibility to residences is found to be approximately five miles away from the centre. The flow of traffic is derived as a spatial pattern and is found to peak approximately three miles from the centre of Manchester. The paper restricts itself to vehicular traffic and to radially symmetric spatial distributions. It should be seen as an attempt to introduce three major elements: time, distribution, and traffic assignment into a geometrical framework for dealing with problems of urban spatial interaction.