A liquid jet issuing from a nozzle may break-up into small drops of a variety of sizes when it is subjected to even minute disturbances due to the phenomenon of capillary instability. With the large number of parameters involved in the description of the jet instability, it should be of great interest to solve the governing equations numerically. Several attempts have been made in this direction and are still very active since a detailed numerical investigation of the break-up of a viscous jet requires a very accurate numerical technique. The present work proposes one such technique capable of an efficient computation of the unknown free surface. It is the stream tube method which uses a transformation of the physical domain. The governing equations are then solved by using an optimisation algorithm. An expected advantage of the method is the easiness in introducing elaborate rheological constitutive equations in order to account for complex fluid behaviour. In this paper, we will give the basic features of the stream tube method in the context of an unsteady jet flow and present the procedures allowing to obtain streamlines and kinematic quantities on the jet instability problem.