In this paper, we present a constant propagation algorithm for explicitly parallel programs, which we call the Concurrent Sparse Conditional Constant propagation algorithm. This algorithm is an extension of the Sparse Conditional Constant propagation algorithm. Without considering the interaction between threads, classical optimizations lead to an incorrect program transformation for parallel programs. To make analyzing parallel programs possible, a new intermediate representation is needed. We introduce the Concurrent Static Single Assignment (CSSA) form to represent explicitly parallel programs with interleaving semantics and synchronization. The only parallel construct considered in this paper is cobegin/coend. A new confluence function, the π-assignment, which summarizes the information of interleaving statements between threads, is introduced. The Concurrent Control Flow Graph, which contains information about conflicting statements, control flow, and synchronization, is used as an underlying representation for the CSSA from.