Geometrical dependence of viscosity of polymethylmethacrylate (PMMA) and high density polyethylene (HDPE) are studied by means of a twin-bore capillary rheometer based on power-law model. Contrary geometrical dependences of shear viscosity are observed for PMMA between 210 and 255°C, but similar geometrical dependences are revealed for HDPE between 190 and 260°C. The fact that wall slip can not successfully explain the irregular geometrical dependence of PMMA viscosity is found in this work. Then, pressure effect and dependence of fraction of free volume (FFV) on both pressure and temperature are proposed to be responsible for the geometrical dependence of capillary viscosity of polymers. The dependence of shear viscosity on applied pressure is first investigated based on the Barus equation. By introducing a shift factor, shear viscosity curves of PMMA measured under different pressures can be shifted onto a set of parallel plots by correcting the pressure effect and the less shear-thinning then disappears, especially at high pressure. Meanwhile, the FFV and combining strength among molecular chains are evaluated for both samples based on molecular dynamics simulation, which implies that the irregular geometrical dependence of PMMA viscosity can not be attributed to the wall slip behavior. © 2013 Wiley Periodicals, Inc. J. Appl. Polym. Sci., 2014, 131, 39982.