Stopping distance and stopping redundancy of product binary linear block codes is studied. The relationship between stopping sets in a few parity-check matrices of a given product code C and those in the parity-check matrices for the component codes is determined. It is shown that the stopping distance of a particular parity-check matrix of C, denoted H_p, is equal to the product of the stopping distances of the associated constituent parity-check matrices. Upper bounds on the stopping redundancy of C is derived. For each minimum distance d=2^r, r≥1, a sequence of [n, k, d] optimal stopping redundancy binary codes is given such k/n tends to 1 as n tends to infinity.