Experimental squeeze flow results show that the behaviour of concentrated short fibre suspensions and concentrated long fibre suspensions impregnated with polymer melts are qualitatively different. Short fibre suspensions have a low yield stress, have an overall squeeze pressure independent of the fibre length, but gap dependent. In contrast, long fibre suspensions have a higher yield stress and their squeeze pressure is proportional to the square of the fibre length, but is gap independent. In both types of suspensions the squeeze pressure is related to the flow behaviour of the pure polymer matrix. An existing model for yield stress fluids is used to predict the squeeze pressure of short fibre suspensions, whereas a new empirical model is proposed for the long fibre suspensions based on fibre–fibre interaction measurements at fibre–fibre contacts. This investigation suggests that for short fibre suspensions the flow profile is a combination of shear-like flow in the core and Coulomb friction at the plates walls, and that the profile becomes more plug-like as the fibre length is increased. This is related to the increasing amplitude of the yield stress.