Pipeline systems in aircraft are connected to the airframe through numerous clamps. There are multiple excitation points and the excitation frequency range is wide, being influenced by accessories such as valves and flanges. To analyse this situation, the method of reverberation ray matrix (MRRM) is extended by random vibration theory to the steady-state random response analysis of a three-dimensional multi-span hydraulic pipeline under multi-point base excitations. Advantages of this approach are that less computational effort is required, cross-correlations between excitations are automatically included, and each response of the system has an exact and unified solution scheme. Each span is represented by the Timoshenko beam model, considering the influence of internal fluid, axial force and pressure of the pipeline, as well as clamps and accessories. An accurate steady-state wave solution for the displacement and internal force of the three-dimensional hydraulic pipeline is derived. The method utilises the analytical characteristics of MRRM and is not limited by the frequency range. Numerical examples demonstrate high accuracy and computational efficiency over a broad frequency range by comparison with random vibration analysis based on the finite element method for a section of hydraulic pipeline subjected to a wide range of random excitation. A systematic parametric study for the hydraulic pipeline system investigates the influences of various boundary conditions, fluid velocity and multi-point excitation coherence.