High combustion temperatures and long operation durations require the use of cooling techniques in liquid propellant rocket engines. For high-pressure and high-thrust rocket engines with long operation times, regenerative cooling is the most preferred cooling method. In regenerative cooling, a coolant flows through passages formed either by constructing the chamber liner from tubes or by milling channels in a solid liner. Traditionally, approximately square cross sectional channels have been used. However, recent studies have shown that by increasing the coolant channel height-to-width aspect ratio, the rocket combustion chamber hot-gas-side wall temperature can be reduced significantly. In this study, the regenerative cooling of a liquid propellant rocket engine has been numerically simulated. The engine has been modeled to operate on a LOX/GH(2) mixture at a chamber pressure of 68 atm and LH2 (liquid-hydrogen) is considered as the coolant. A numerical investigation was performed to determine the effect of different aspect ratio cooling channels and different coolant mass flow rates on hot-gas-side wall temperature and coolant pressure drop. The variables considered in the cooling channel design were the number of cooling channels and the cooling channel cross-sectional geometry along the length of the combustion chamber.