By using the method of Laplace Transformations in solving the partial differential equations an exact solution to the problem of non stationary rectilinear flow of viscous fluid through a circular pipe for the case when a linear dépendance exists between the pressure and the flow rate at the pipe beginning has been presented. Here the case when a parabolic dependence between the pressure and the flow rate exists at the beginning of the pipe has also been considered. Finally., an approximate solution to the problem has been also presented, assuming that there is laminarity of the non stationary flow, similarly to the case of stationary laminar flow of a viscous fluid throught a pipe.