Transient pressure traces as recorded with a prototype injection rheometer exhibit overshoots during the early period of injection shots of glass fibre filled polybutylene terephthalate (GF-PBT) whereas the virgin polymer gives steady pressure growth traces. A modelling is proposed that considers the superposition of two events: A smooth pressure growth associated with the flow development of the virgin polymer, and a pulse pressure consumption as fibres, initially randomly oriented, align themselves along the developing flow paths, The model is applied to experimental data through non-linear regression techniques and a good agreement is observed, An interesting aspect of the approach is that it is not necessary to refer to non-linear viscoelasticity to explain the behaviour of GF-PBT.