<p>Propellant feedlines in liquid-propellant rocket engines (LPREs) are complex and diverse. Certain LPRE configurations involve switching the propellant flow from an initial start-up line to the primary feedline during engine start-up. This study aims to develop a systematic approach to the mathematical modeling of dynamic processes in such reconfigurable hydraulic systems, using a staged combustion cycle restartable LPRE designed by the private aerospace company Flight Control Propulsion as a case study. This approach is based on matching the frequency characteristics of different branches of the reconfigurable hydraulic system, obtained using the impedance method from both distributed- and lumped-parameter models. Mathematical modeling results show that during the transition of fuel feed from the starting tank to the pump, the fuel flow to the combustion chamber remains stable, while the flow to the preburner ranges from 62 to 200%. It is noted that the mathematical model for calculating transient processes in the reconfigurable hydraulic system can serve as an effective tool for improving the design of the check valve and optimizing the fuel feed system characteristics. It is demonstrated that integrating an additional orifice in the fuel line between the starting tank and the preburner reduces the fuel flow range to the preburner by more than 30%. Additionally, simultaneously reducing the initial preload force of the check valve poppet spring by 50% and increasing the spring stiffness by 50% effectively eliminates oscillatory motion of the check valve poppets during engine start-up.</p>