As the number of available multiprocessors increases, so does the importance of providing software support for these systems, including parallel compilers. Data flow analysis, an important component of software tools, may be computed many times during the compilation of a program, especially when compiling for a multiprocessor. Although converting a sequential data flow algorithm to a parallel algorithm can present some opportunities for computing data flow in parallel, more parallelism can be exposed by the development of new parallel data flow algorithms. We present a technique that computes rapid data flow problems in parallel and thus is applicable for commonly used classical data flow problems, including reaching definitions, reachable uses, available expressions, and very busy expressions. Unlike previous techniques, our technique exploits the inherent parallelism in the data flow computation that occurs across independent paths, within linear paths, and in paths through loops of a control flow graph. The technique first changes cyclic structures in a control flow graph to acyclic structures and then builds a combining directed acyclic graph (DAG) that represents the paths through the control flow graph needed to compute data flow. Data flow is then computed using two passes over the DAG by computing the data flow for the nodes on each level of the DAG in parallel. We also present experimental results comparing the performance of our algorithm with a sequential algorithm and a parallelized sequential algorithm.>