An experimental and a theoretical study were carried out to determine the stress distributions of viscoelastic polymeric melts in a converging channel. For the experimental study, two different types of experiment were conducted using converging channels: one was the measurement of wall normal stress with the aid of pressure transducers, and the other was the measurement of stress birefringence with the aid of a circular polariscope, which enabled us to determine both shear stress and normal stress distributions in the channel. It was found that the distribution of wall normal stress goes through a minimum and that the extensional stresses along the centerline of the converging channel determined from the stress birefringence patterns, go through a maximum. For the theoretical study, the Coleman‐Noll second‐order fluid was used to derive theoretical expressions for the wall normal stress, and shear and normal stresses in the converging flow field. It was found that the theoretical analysis corroborates qualitatively the experimentally determined stress distributions.