This work concerns external gear pumps for automotive applications, which operate at high speed and low pressure. In this context, a non-linear lumped kineto-elastodynamic model was developed, with the aims to including all the main dynamic effects while maintaining a rather simple model. The model has six degrees of freedom and takes into account the parametric excitations due to the time-varying meshing stiffness. Moreover, the oil pressure distribution on gears is also time-varying: it is instantaneously computed and the resultant force and torque are obtained. All the mentioned excitations vary periodically with a period equal to the gear meshing period. Finally, the non-linear behaviour of the hydrodynamic journal bearings is included, as well as the torsional stiffness and damping of the driving shaft. The differential equations of motion are numerically integrated. In addition a linear model for each operation condition was developed obtaining the natural frequencies and modes.