Interconnection networks provide an effective mechanism for exchanging data between processors in a parallel computing system. Graph embedding problems have gained importance in the field of interconnection networks. In this paper, we determine the congestion and wirelength of embedding complete bipartite graphs K2mn,2mn into grids M[2m × 2n], m ≤ n and cylinders P2m × C2n, m ≤ n. Copyright © 2017 Inderscience Enterprises Ltd.