AbstractRecently developed block‐iterative versions of some row‐action algorithms for solving general systems of sparse linear equations allow parallelism in the computations when the underlying problem is appropriately decomposed. However, problems associated with the parallel implementation of these algorithms have to be addressed.In this paper we present an implementation on distributed memory multiprocessors of a block version of the Kaczmarz row‐action method. One of the main issues related to the efficient implementation of this method on a concurrent environment is to develop suitable communication schemes in order to reduce the amount of communication needed at each iteration.We propose two data distribution strategies which lead to different computation and communication schemes.To verify and compare the effectiveness of the proposed strategies, numerical experiments have been carried out on a Symult S2010 and a Meiko Computing Surface. The performance evaluation has been done using a scaled efficiency