A parallel unstructured grid generation algorithm is presented and implemented on the INTEL hypercube. Different processor hierarchies are discussed, and the appropriate hierarchies for mesh generation and mesh smoothing are selected. A domain-splitting algorithm for unstructured grids, which tries to minimize the surface-to-volume ratio of each subdomain, is described. This splitting algorithm is employed both for grid generation and grid smoothing. Results obtained on the INTEL hypercube demonstrate the effectiveness of the algorithms developed.