In this paper a numerical simulation of the drop formation in drop-on-demand ink-jet print head devices is described. Different pressures histories are considered and a finite difference technique is used to obtain the velocity profile at the exit of the nozzle. For the computation of the unknown free surface shape, we propose an efficient technique based on the stream-tube method, which has been used elsewhere essentially for simulating extrusion problems for which the effect of surface tension is negligible.The distinguishing features of the proposed method in contrast to other codes are the easiness in introducing elaborate rheological constitutive equations in the model and the limited amount of computer resources, which is necessary. The results obtained simulate drop formation from a nozzle for different specified driving pressures and cover both the inviscid and the viscous cases.They reveal the essential features namely the transient evolution of the velocities and the pressures inside the filament that lead to the pinch-up of the drop. Finally, the numerical results are discussed in the light of drop formation experiments.