Pointer analysis is essential for optimizing and parallelizing compilers. It examines pointer assignment statements and estimates pointer-induced aliases among pointer variables or possible shapes of dynamic recursive data structures. However, previously proposed techniques are not able to gather useful information or have to give up further optimizations when overall recursive data structures appear to be cyclic even though patterns of traversal are linear. The reason is that these proposed techniques perform pointer analysis without the knowledge of traversal patterns of dynamic recursive data structures to be constructed. This paper proposes an approach, {\em traversal-pattern-aware pointer analysis}, that has the ability to first identify the structures specified by traversal patterns of programs from cyclic data structures and then perform analysis on the specified structures. This paper presents an algorithm to perform shape analysis on the structures specified by traversal patterns. The advantage of this approach is that if the specified structures are recognized to be acyclic, parallelization or optimizations can be applied even when overall data structures might be cyclic. The DEF/USE information of pointer statements is used to relate the identified traversal patterns to the pointer statements which build recursive data structures. (Also cross-referenced as UMIACS-TR-97-66)