We present a parallel algorithm of the overlapping domain decomposition boundary integral equation method for two dimensional partial differential equations. Besides the improvement of the ill-conditioning and the computational efficiency achieved from domain partitioning, using a parallel computer with $p$ processors can offer up to $p$ times efficiency. Assuming direct solution is used throughout, partitioning the domain into $p$ subregions and employing a processor for each subproblem, overall, result in $p^2$ times efficiency over using a single domain and a single processor, taking into account that a sequential algorithm of the underlying method can improve the computational efficiency at least $p$ times over a single domain. Some numerical results showing the efficiency of the parallel technique will be presented.
