In this paper we study the problems of sorting and selection on the Distributed Memory Bus Computer (DMBC) recently introduced by Sahni. In particular we present: 1) An efficient algorithm for computing the sum ofnbits; 2) An optimalO(1) time sorting algorithm; 3) An optimal randomized logarithmic lime integer sorting algorithm; and 4) An optimal randomized constant time selection algorithm. Our algorithms will run without change in performance on many related models as well. For example, these algorithms apply to the RMBM model of Vaidyanathan et al.