Abstract This paper presents a novel multi-objective model of active distribution network planning based on stochastic programming and uncertain random network (URN) theory. The planning model is proposed to find the final scheme with optimal alternative, location, size and operational strategy for the candidate distribution lines, transformer substations (TSs), distribution generations (DGs), static var compensators (SVCs) and on-load tap changers (OLTCs). Firstly, a scenario-based approach is developed to analyse the uncertainties in network system, such as the demand and intermittency of renewable sources. Since the impact of multiple uncertain factors on network cannot be ignored, a network frame is then modelled by uncertain and random weights of spanning tree (ST) instead of fixed value. In order to achieve the minimization of total cost, and further the selection of a minimum spanning tree (MST) with the uncertain and random weight, a 3-dimensional uncertain space is constructed based on the combination of the previous two targets. In addition, a second-order cone programming (SOCP) is applied to cope with the multi-objective, mixed-integer nonlinear nature of the proposed planning model. Simulation is performed on a modified Pacific Gas and Electric Company (PG&E) 69-bus distribution system, and the results demonstrate the effectiveness of the proposed model.