It is well known that sparse matrix-vector multiplication is the central part of many numerical algorithms, especially iterative solvers for systems of linear equations. In case of distributed memory parallel computers, the performance of such solvers can be improved when we design a suitable distribution of the data and the associated work. The authors present a 2D method for partitioning sparse matrices and a method for partitioning the input and the output vectors that attempts to balance the communication volume among processors. The method is based on a recursive bipartitioning of the sparse matrix by splitting it into two parts with a nearly equal number of nonzero elements. Numerical tests of the method with respect to a set of sparse test matrices are also presented and discussed. The paper is also an excellent introduction to sparse matrices on parallel computers.