A parallel technique, for a distributed memory machine, based on domain decomposition for solving the Navier-Stokes equations in cartesian and cylindrical coordinates in two dimensions with free surfaces is described. It is based on the code by Tome and McKee (J. Comp. Phys. 110 (1994) 171-186) and Tome (Ph.D. Thesis, University of Strathclyde, Glasgow, 1993) which in turn is based on the SMAC method by Amsden and Harlow (Report LA-4370, Los Alamos Scientific Laboratory, 1971), which solves the Navier-Stokes equations in three steps: the momentum and Poisson equations and particle movement, These equations are discretized by explicit and 5-point finite differences. The parallelization is performed by splitting the computation domain into vertical panels and assigning each of these panels to a processor. All the computation can then be performed using nearest neighbour communication. Test runs comparing the performance of the parallel with the serial code, and a discussion of the load balancing question are presented. PVM is used for communication between processes. (C) 1999 Elsevier B.V. B.V. All rights reserved.