Pick-up and delivery services are essential for businesses in urban areas. However, due to the limited space in city centers, it might be unfeasible to provide sufficient loading/unloading spots. As a result, this type of operations often interferes with traffic by occupying road space (e.g., illegal parking). In this study, a potential solution is investigated: Dynamic Delivery Parking Spots (DDPS). With this concept, based on the time-varying traffic demand, the area allowed for delivery parking changes over time in order to maximize delivery opportunities while reducing traffic disruptions. Using the hydrodynamic theory of traffic flow, we analyze the traffic discharging rate on an urban link with DDPS. In comparison to the situation without delivery parking, the results show that although DDPS occupy some space on a driving lane, it is possible to keep the delay at a local level, that is, without spreading to the network. In this paper, we provide a methodology for the DDPS design, so that the delivery requests can be satisfied while their negative impacts on traffic are reduced. A simulation study is used to validate the model and to estimate delay compared to real situations with illegal parking, showing that DDPS can reduce system's delay.