A new approach has been adopted to study the sharkskin phenomenon and to characterize the extrudate surface roughness observed in polymer melt extrusion of a linear low‐density polyethylene through capillary dies. A previously proposed method, for the calculation of slip velocities as a function of both wall shear stress and pressure, was extended for polymer melts with a pressure‐dependent viscosity. In this work, the surface roughness of solidified extrudate samples was analyzed by means of digital image processing techniques. The fractal dimension of the extrudate surface was used as a quantitative measure of roughness and the effect of the wall shear stress on the severity of the sharkskin phenomenon was studied. The onset of surface roughness could be directly determined and it was found to lag behind the onset of slip in the die. The main advantage of the present method is the scale independence of the roughness measure. In addition, since only digital images of extrudates are required for the detection of surface roughness and due to short processing times involved, this method could potentially be employed in on‐line monitoring systems for the production of films with controlled roughness.