A parallel algorithm for the simulation of steady-state, two-dimensional flows of integral viscoelastic fluids on Multiple Instruction Multiple DATA (MIMD) computers with distributed memory is proposed. The algorithm has been implemented within the commercial finite element package POLYFLOW developed at Louvain-la-Neuve and widely used in polymer processing applications. Parallel performance results obtained on the Intel iPSC/860 hypercube are discussed for the flow of a K.B.K.Z. fluid through an abrupt contraction. It is found that satisfactory levels of parallel speed-up can be obtained by using a rather simple allocation scheme to schedule workload to the available processors. The optimal use of the parallel computer requires, however, a dynamic load allocation scheme. An adaptive strategy that reallocates the workload to the processors has been proposed on the basis of the history of the nonlinear iterative process. The proposed adaptive allocation scheme is found to carry only marginal compute and communication overheads.