This paper concerns the static analysis of programs that perform destructive updating on heap-allocated storage. We give an algorithm that conservatively solves this problem by using a finite shape-graph to approximate the possible “shapes” that heap-allocated structures in a program can take on. In contrast with previous work, our method M even accurate for certain programs that update cyclic data structures. For example, our method can determine that when the input to a program that searches a list and splices in a new element is a possibly circular list, the output is a possibly circular list.