Modeling the evolution of the state of program memory during program execution is critical to many parallelization techniques. Current memory analysis techniques either provide very accurate information but run prohibitively slowly or produce very conservative results. An approach based on abstract interpretation is presented for analyzing programs at compile time, which can accurately de- termine many important program properties such as aliasing, logical data structures and shape. These properties are known to be critical for transforming a single threaded program into a version that can be run on multiple execution units in parallel. The analysis is shown to be of polynomial complexity in the size of the memory heap. Experimental results for benchmarks in the Jolden suite are given. These results show that in practice the analysis method is efficient and is capable of accurately determining shape information in programs that create and manipulate complex data structures.