To incentivise citizens to return recyclable waste (RW) through formal recycling channels, the Chinese government has introduced smart recycling facilities for RW. To maximise the satisfaction of citizens’ demand for returning RW, the proper arrangement of recyclable facilities is a problem worth studying in cases in which there is a lack of data on the citizens’ behaviour. Thus, to help government decision-makers rationally arrange smart recycling facilities, this paper discusses how to properly allocate the recycling infrastructure to cover the maximum demand with a limited number of smart recycling facilities in an uncertain environment. According to the uncertainty theory, the service cost is taken as an uncertain variable. Then, an uncertain maximal covering location problem model and an extended uncertain maximal covering location problem model are constructed, and solution procedures of the two models are provided. The effectiveness of the proposed mathematical formulations and solution procedures were validated through two application cases.