AbstractIt is the object of the present study to obtain clear knowledge of the relations in the polypropylene melt between its linear viscoelasticity and its nonlinear steady capillary flow, paying particular attention to the elastic properties in its capillary flow. By representing the linear viscoelasticity numerically with zero‐shear viscosity, η0, and steady‐state compliance, J, evaluation has been made of the properties concerning the elasticity of polymer melt in the capillary flow, such as non‐Newtonianity, the entrance pressure loss, the end correction, the Barus effect, and the melt fracture. The steady flow viscosity η, the entrance pressure loss P0, the critical shear stress, τc, and the critical shear rate $\dot \gamma _c$ at which melt fracture begins to occur are subject to η0 as follows: From the well‐known relationship between η and the weight‐average molecular weight M̄w, these quantities are governed by M̄w. Meanwhile, for such quantities as structural viscosity index N, end correction coefficient ν, and elastic pressure loss ratio P0/P, following correlations hold: As η0 and J are respectively determined mainly by M̄w and the molecular weight distribution MWD, these quantities are governed by both M̄w and MWD. Physical meanings of η0·J and η02 · J are, respectively, mean relaxation time and a measure of stored energy in steady flow. The Barus effect has a positive correlation to J, ν, and P0/P. (The symbol ∝ employed here means positive correlation.)