We apply four stress-velocity-pressure algorithms to calculate four benchmark problems, i.e., the flow of a Maxwell fluid around a sphere, through a wavy tube, through an abrupt contraction, and in circular extrusion. For every flow, we use only one mesh, i.e., the same number of velocity nodes and the same boundary conditions for all algorithms. The meshes are neither too coarse nor too refined in order to provide us with a practical evaluation of the methods, i.e., a simple mixed method MIX0, the 4 X 4 element, and two types of interpolation for elastic-viscous split stress (EVSS). We also investigate three methods of integration of the constitutive equations : Galerkin, SUPG, and SU. The performance of 4 X 4 and the high-order EVSS are about the same. It is shown that the performance of MIX0 can be remarkably stable and accurate with smooth problems or leads to very poor results in more difficult cases. The low-order EVSS method is accurate, stable, and cheap in computer time. It should be a good candidate for three-dimensional developments.