Ever since the development of liquid rocket engine, there has been a need to predict the peak heat flux that affects the engine material and thus to control the wall thermal behavior of rocket engine. To prevent thermal failure, the engine is generally cooled by means of a coolant that flows in passages that line the hottest part of the engine (i.e., combustion chamber and nozzle wall). This is the fluid-cooling system. If the coolant is one of the propellants, once it passes through the cooling circuit, it can be injected into the combustion chamber or it can be dumped overboard. The former case is referred to as Regenerative cooling system while the latter as dump cooling system. In case of high performance cryogenic rocket engine (such as LO2/hydrogen and LO2/methane engines) the coolant working pressure is supercritical and thus it behaves far from a liquid or a perfect gas. The fluid-cooling system (often referred to regenerative cooling because of the limited application of the dump cooling) of cryogenic rocket engines, is the technological background of this Ph.D. thesis. It is common and well confirmed practice in industry to analyze wall thermal behaviour of liquid rocket engine by means of simple and fast tools based on semi-empirical relationships. These relationships are generally calibrated by means of data collected in experimental tests of subscale engines. Industrial tools provide reasonable results but they are not able to accurately describe many phenomena that occur in the hot-wall/coolant environment, such as three-dimensional effects, asymmetric heat flux distribution in the material and supercritical behaviour of the coolant. For that reason, to circumvent the uncertainties of the design tools, regenerative systems are often over dimensioned. Moreover, these tools are deeply related to the engine for which they have been calibrated and thus they cannot be easily extended for a new generation of engines. In last years new approaches have risen; in fact new geometry configuration (i.e., high aspect ratio cooling channels) and new coolants (such as methane) to be used in the next future, have imposed more accurate analysis tools, such as three-dimensional Navier Stokes solver to describe coolant flow and three-dimensional Fourier analysis to describe wall thermal transmission. Simplified approaches are always used since, due to the limited computer power, three-dimensional tools are not suitable as design tools. However, accurate three-dimensional analysis can be integrated with simple and fast design tool in order to better describe and comprehend the phenomena that occur in the hot-wall/coolant environment. The aim of this study is to present and provide suitable theoretical and numerical tools able to describe the thermal behaviour that occur in regenerative cooling system, with special regard to the subcritical/supercritical coolant flow inside cooling channels. This aim has been achieved in three steps: A suitable mathematical description of thermophysical properties of coolants has been adopted. According to this mathematical modeling, computer subroutines describing the thermophysics of typical coolants (such as hydrogen and methane) have been implemented; A suitable physical and mathematical model able to describe both the wall thermal behaviour and the coolant flow that occur in regeneratively cooled rocket engines has been developed and implemented in a numerical code. The model is an extension of the typical 1D-model in the sense that it is able to describe the coolant and fin thermal stratification that occurs in high aspect ratio cooling channels. For that reason this model will be referred to as a quasi-2D model. The coolant thermophysical properties have been provided by means of the above mentioned hydrogen-methane subroutines. The code has been successfully validated with respect to the literature data; At last, a Navier-Stokes solver able to describe the high Reynolds number turbulent flow of generic fluid in three-dimensional cooling channels has been developed. This numerical tool has been successfully validated by comparison with exact solutions and literature data. Furthermore three-dimensional flow fields for a cryogenic fluid (methane) have been computed to analyze the coolant behavior inside straight channels with rectangular cross section and to discuss the channel aspect ratio effect on the cooling performances.