There has been much research on enhancing the performance of database operations in hypercube multicomputer systems. Among them, the join operation is one of time consuming operations in relational database systems. Although many parallel join algorithms have been proposed in the past, the performance characteristics of those algorithms are highly affected by the distribution of tuple values and the size ratios of two relations to be joined. In this thesis we propose an efficient paralle relational join algorithm, called Cube Robust, on a hypercube multicomputer which is robust in size ratios of two relations to be joined. We develop analytic cost models for various parallel join algorithms on hypercube multicomputer systems. We show through performance comparisons that the Cube-Robust join algorithm works better than other provious join algorithms in a wide range of size ratios.