Algorithms for efficient implementation of computation of prefix produce on mesh-connected processor arrays are presented. Assuming that an arithmetic operation takes unit time and communication/computation ratio for a single input item isτ, we show that the prefixes ofnitems can be computed in time 2τ√n + O(logn) on a square mesh withnprocessors. Ifnprocessors are configured as a disc with respect to the Manhattan metric, then the parallel time for the problem becomes √2τ√n + O(√τ4√n. We show that both of these algorithms are asymptotically optimal.