The aim of this research is to develop optimal packet routing strategies for the Mesh Hypercube (MH) network of arbitrary size. MH has been introduced as a new interconnection network for multicomputer systems. The basic structure for this network is a combination of both mesh and hypercube networks. In this research, the parallel path property in the MH is studied and the length and the number of parallel shortest paths are computed. An optimal packet routing algorithm is given which uses minimal length path. The algorithm is simple and appears to be well suited to VLSI implementation. The simulation results of the proposed algorithm on various network designs showed that it performs very well at various network conditions. In a MH of size mn nodes, the algorithm performs outstandingly when nm. Specifically, the best results of both waiting-time and packet-latency network performance measures were achieved when m=4 and n=16, while the worst values of all measures were obtained when m=8 and n=8.