Distribution networks contain a large number of components and, in many cases, the required data for network modeling are often missing or uncertain. In order to circumvent the problem of dealing with uncertain data, uncertainties in network parameters and feeder node injections are handled by using the “unknown but bounded” scheme. A possibility approach used to take into account the effects of uncertainties in distribution system state estimation is proposed in this paper. In the proposed estimation approach, all possible solutions within bounds are considered. Test results have shown that this approach can handle various uncertainties that exist in the network model and the solutions obtained can provide useful information for distribution system operations.