An analysis of the flow of a second-order fluid is presented. Reference values for some variables are defined, and with these a non-dimensional formulation of the governing equations. From this formulation, three dimensionless numbers appear; one is the Reynolds number, and two numbers that are called the first-and second-dimensionless normal stress (NSD) coefficients. The equations of motion are solved by a finite element method using a commercially available program (Fidap), and the steady state converged solution was used to measure the die swell. The factors that influence die swell and that are studied in this work include: the die geometry for circular cross sectional dies, including tubular, converging, diverging, half-converging/half-tubular shapes; fluid characteristics such as Reynolds number and first-and second-DNS coefficients (both positive and negative values); and flow rates, as determined by the maximum velocity in a parabolic velocity profile at the entrance to the die. The results suggest that shear and deformation histories of the fluid directly influence not only swell characteristics, but also convergence characteristics of the numerical simulation.