Viscoelastic constitutive equations are evaluated using the benchmark problem of the planar flow past a confined cylinder for a well‐characterized solution of 5%(w/w) polyisobutylene in tetradecane. The ratio of channel height to cylinder diameter is equal to two. We compare finite element simulations with point‐wise measured velocities and stresses obtained by means of laser Doppler anemometry and a flow‐induced birefringence technique, respectively. The Deborah number (De) ranges from 0.25 to 2.32. In the case of the geometry with a symmetrically confined cylinder, computations were made with a generalized Newtonian model and with both a single‐ and a four‐mode Phan‐Thien and Tanner (PTT) model. All model parameters were determined in simple shear flow. A similar analysis is presented in case of an asymmetrically confined cylinder (with De=1.87). Impressively good agreement was found between the predictions of the four‐mode PTT model and the measured velocities and stresses. The agreement was even excellent in the geometry with the asymmetrically confined cylinder.