Planar Stokes flow of a concentrated planar suspension of rigid cylinders is simulated using the finite-element method. A constraint condition, limiting cylinder approach to a specified distance, is applied to simulate interparticle contacts. The results of these simulations reveal a stress response and ordering of the cylinders which is similar to experimental observations of suspensions of nominally spherical particles. These results include direct observations of anisotropic structure, as well as the development of a distinct particle-phase pressure resulting from the asymmetry of interparticle contacts and the consequent developed anisotropy. A simple pair-wise interaction model is proposed forab initioprediction of the particle-phase pressure for these planar suspensions of cylinders.