Previous emergency service covering models consider all the calls to be of the same importance and impose the same waiting time constraints independently of the service's priority. This type of constraint is clearly inappropriate in many contexts. For example, in urban medical emergency services, calls that involve danger to human life deserve higher priority over calls for more routine incidents. A realistic model in such a context should allow prioritizing the calls for service. In this paper a covering model which considers different priority levels is formulated and solved. The model inherits its formulation from previous research in Maximum Coverage Models and incorporates results from Queuing Theory, in particular Priority Queuing. The additional complexity incorporated in the model justifies the use of a heuristic procedure. An exhaustive evaluation of the heuristics, based in simulated networks, is developed and a numerical example illustrates the functionality of the model. Results are compared with those obtained with a model that does not consider different priorities.