To help better evaluate the safety and utilization of distribution networks， a linear programming-based approach to obtaining the maximum utilization ratio of distribution systems with arbitrary topologies and capacities is put forward. A series of safety indices considering load variation are proposed， including the real-time utilization ratio， real-time shortage ratio， averaged utilization ratio， averaged shortage ratio， N-1 criterion meeting to duration ratio， N-1 criterion meeting， N-1 criterion meeting risk， and regulating ratio of N-1 criterion meeting critical load. The steps of evaluation are suggested. Several examples are given to illustrate typical applications of the approaches proposed showing that it is feasible and can provide more information to planning， operation and engineering of distribution systems. It is also shown that the indices of utilization and extent for meeting N-1 criterion can be improved by optimizing the allocation of the sectionalizing switches on the feeders.