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X10 is a modern object-oriented programming language designed for high performance, high productivity programming of parallel and multi-core computer systems. Compared to the lower-level thread-based concurrency model in the JavaTM language, X10 has higher-level concurrency constructs such as async, atomic and finish built into the language to simplify creation, analysis and optimization of parallel programs. In this paper, we introduce a new algorithm for May-Happen-in-Parallel (MHP) analysis of X10 programs. The analysis algorithm is based on simple path traversals in the Program Structure Tree, and does not rely on pointer alias analysis of thread objects as in MHP analysis for Java programs. We introduce a more precise definition of the MHP relation than in past work by adding condition vectors that identify execution instances for which the MHP relation holds, instead of just returning a single true/false value for all pairs of executing instances. Further, MHP analysis is refined in our approach by using the observation that two statement instances which occur in atomic sections that execute at the same X10 place must have MHP = false. We expect that our MHP analysis algorithm will be applicable to any language that adopts the core concepts of places, async, finish, and atomic sections from the X10 programming model. We also believe that this approach offers the best of two worlds to programmers and parallel programming tools ---higher-level abstractions of concurrency coupled with simple and efficient analysis algorithms.