Information about which statements in a concurrent program may happen in parallel ( MHP ) has a number of important applications. It can be used in program optimization, debugging, program understanding tools, improving the accuracy of data flow approaches, and detecting synchronization anomalies, such as data races. In this paper we propose a data flow algorithm for computing a conservative estimate of the MHP information for Java programs that has a worst-case time bound that is cubic in the size of the program. We present a preliminary experimental comparison between our algorithm and a reachability analysis algorithm that determines the “ideal” static MHP information for concurrent Java programs. This initial experiment indicates that our data flow algorithm precisely computed the ideal MHP information in the vast majority of cases we examined. In the two out of 29 cases where the MHP algorithm turned out to be less than ideally precise, the number of spurious pairs was small compared to the total number of ideal MHP pairs.