This thesis work has been carried out partly in conjunction with the Institute of Propulsion Technology of the German Aerospace Center, DLR, in Cologne, Germany. The subject is simulation of fluid flow and hydrogen combustion in a so-called scramjet engine. Scramjet is an acronym for Supersonic Combustion Ramjet, a novel type of propulsion device, interesting primarily for potential spaceflight applications. The aim is to give an indication of how fluid flow and fuel combustion proceed when both mixing and combustion are carried out at supersonic speeds, and to provide a validation of two different solver packages for fluid dynamical problems. In this study, Reynolds-averaged Navier-Stokes models (RANS) have been used to examine supersonic flow and combustion in a model scramjet combustion chamber. The RANS-model is based on a finite volume discretization of the continuity, momentum, energy and mixture fraction equations. The configuration used is a model of a laboratory scramjet combustor at the Institute for Space Propulsion at DLR. It consists of a divergent channel with a flame-holding, wedge-shaped structure in the middle of the flow field from the base of which hydrogen is injected. Three different operational cases with varying degree of complexity have been investigated. For the purpose of validation of the simulation models the results are systematically compared with experimental data for temperature, velocity and pressure at certain cross- sections in the combustion chamber. Qualitative comparisons are also made between the simulated flow fields and experimental schlieren and shadowgraph fields. The simulation codes used are ANSYS CFX and a solver program for fluid dynamics and combustion chemistry developed by my supervisor at DLR. Each simulation model is capable of predicting both the cold supersonic flow and the reacting flow fields reasonably well, with some quantitative inconsistencies for both models. Moreover, during the work a previously undiscovered deficiency in the non-commercial code is found, which leads to an appreciated improvement of the program.