Purpose. The paper studies the progressive occupancy of parking capacity along the street by candidate users, under the user equilibrium paradigm. The situation depicted typically applies to a parking peak period. Methods. In our model, the parking supply is made up of capacitated lots situated along a spatial axis, while the demand is disaggregated continuously in both destination place and preferred time of arrival. Each user selects a parking lot and time from among options on the basis of their trade-offs between walking, driving, parking price and schedule delay. Efficient algorithms are developed and an application instance is dealt with in detail. Results. The dynamical equilibrium pattern exhibits parking lots “efficiency regions” in the plane of destination places and preferred arrival times. These efficiency regions are dynamic market areas with strong yet simple structural characteristics, making it easy to assign each parking user to his preferred option and to derive the lot saturation times. The latter are identified as the key state variables for the parking system, since they induce the lot efficiency regions. The equilibrium state is characterized as the solution to a fixed-point problem with respect to the saturation times. Conclusion. Our model improves upon previous parking models in economic theory, by adopting a higher resolution in space and time on both supply and demand side. The higher resolution is enabled by focusing on the street level, thus restricting the outreach of the model. Further research may be directed to extend the model to a network of streets, on the side of traffic assignment, and to study parking management policies, on the side of parking economics.