An implementation of the primal-dual predictor-corrector interior point method is specialized to solve linear multicommodity flow problems. The block structure of the constraint matrix is exploited via parallel computation. The bundling constraints require the Cholesky factorization of a dense matrix, where a method that exploits parallelism for the dense Cholesky factorization is used. The resulting implementation is 65 to 90 percent efficient, depending on the problem instance. For a problem with K commodities, an approximate speedup for the interior point method of 0.8K is realized.