The importance of transient analysis in hydraulic networks has been well recognized due to abrupt changes in flow or pressure introduced by valve closures or component failures. Therefore, accurate and robust numerical models are necessary to analyse the travelling pressure waves as a result of such sudden changes. This paper presents the formulation of a semi-analytical impulse response method applied to transient laminar flow in hydraulic networks. The method is based on the exact solution of a two-dimensional viscous model in the frequency domain with various interface and boundary conditions. The numerical computation is based on the use of the fast Fourier transform and the discrete numerical convolution with respect to time. To illustrate the method, a numerical example is presented and the results are compared with the method of modal approximations that is widely used in practice. The results show that the proposed method is able to predict the transient behaviour with better accuracy and without the need of spatial discretization. Thus, it is expected that for large networks, the computational cost of the impulse response method will have a great advantage when compared to existing grid-space methods.