This paper is a compilation of the research efforts of five different groups (Bertin Technologies and CNES, IMFT, ONERA, Purdue University and Technische Univer- sität München) on the prediction of combustion instabilities in a model rocket engine. This research was initiated by the REST group (Rocket Engine Stability iniTiative) for the 2nd REST Workshop on Combustion Instability Modeling, which took place in October 2010 at Astrium GmbH in Ottobrunn. The target experiment consists of a single shear coaxial injector using methane and decomposed hydrogen peroxide as reactants. Both the inlet of the injector and the outlet of the chamber are choked, resulting in well-defined acoustic boundary conditions. The length of the oxidizer tube could be varied continuously and its influence on the stability is studied. Many numerical strategies were tested, addressing different physical phenomena at play during unstable combustion. Acoustic solvers, both with and without mean-flow effects were used to draw stability maps. The weak spot of these solvers is that they require the flame response to acoustic perturbations as an input. Large-Eddy Simulations, requiring no such a priori knowledge, were performed with the intent to elucidate flame stabilization and flame response mechanisms.