A one-dimensional mathematical model is presented for flows in a rocket engine that has a regenerative cooling system. The problem involves the flow of a gas in a converging- diverging nozzle, the flow of a coolant in channels distributed around the engine, and the heat conduction through a wall between the gas and the coolant. The numerical model adopted is based on the finite-volume method with a second-order scheme. It was noted that it is important to use variable properties in order to predict the maximum wall temperature in the rocket engine and the drop in pressure of the coolant as it moves along the channels, whereas the thrust of the engine can be calculated with constant properties.