One of the most fundamental problems in numerical analysis is finding solutions to simultaneous equations, whether linear or non linear. Iterative methods for finding such solutions have been implemented for the CPU and more recently the GPU. This article, proposes an implementation of the method GMRES using the CUDA architecture for solving linear systems. The before mentioned architecture was introduced in the year 2006 and some algorithms have been successfully implemented for it. In this work, the efficiency of this implementation is compared with versions of the algorithm implemented for different platforms. Finally the advantages and disadvantages of the architecture are evaluated studying the GMRES method, and some future work is proposed.