The H4 robot is a parallel machine with four degrees of freedom. The purpose of this work is to evaluate the H4 stiffness, ie the displacement response of the tool controlled point when it is submitted to a given force using an analytical method. A stiffness analysis based on analytical calculations is performed. It has the advantage to be rather fast and easy to integrate into a design optimization. This method allows to compute stiffness matrix of parallel robots and takes into account particularity of parallel robots with articulated traveling plate. Some numerical results are shown at the end of this paper for the H4 first prototype.