For distribution systems with distribution generations（DGs）， uncertain outputs of DGs are the key factor affects distribution systems service restoration and self-healing. As thus， the DG output and load are described as intervals and an interval load flow based method to calculate the optimal cut-point of tie switches is present. The effects of backup capacity limitation and load distribution on restoration is also considered in the method. A heuristic algorithm for the restoration of distributed systems with DGs is formulated to determine the closing order of the tie switches by optimum cut point calculation. The backup capacity can be fully utilized by this algorithm and the effects of uncertain loads and DG outputs on service restoration can be included. The proposal algorithm is highly valuable for engineering applications. Case studies using a real network is given to verify the effectiveness of the proposed algorithm.