Exit pressure experiments are performed for three low‐density polyethylene melts. Viscosity and exit pressure data are obtained for a shear rate range of 1–350 reciprocal seconds. The measured pressure profiles are fit by both linear and quadratic functions. Extrapolation of the linear pressure profiles yields negative exit pressures which increase in magnitude with shear rate or shear stress. Extrapolation of the quadratic pressure profiles yields small, positive values for the exit pressures. The curvature in the pressure profiles is attributed to the pressure dependence of viscosity. If the data from quadratic pressure profiles is analyzed using the exit pressure theory the estimation of first normal stress difference agrees with independent measurements for shear rates as high as100 s−1.