The study focuses on the full simulation of a multiple coaxial configuration which typifies, on a model scale, the geometry and the thermodynamic and injection conditions found in real rocket engines. Cryogenic reactants (liquid oxygen and gaseous methane) are injected under transcritical conditions, a situation reached when the pressure is higher than the critical pressure of the reactants and the injection temperature is lower than the critical temperature. The dynamics of high-pressure transcritical flames submitted to high-frequency transverse acoustic modes is specifically considered. Calculations are carried out in the exact configuration of a model scale combustor mounted on the Mascotte cryogenic test bench (ONERA and EM2C), operating at 6.7 MPa. This system comprises five shear-coaxial injectors arranged on a line in the chamber backplane and it is equipped with a very high amplitude modulator (VHAM). This device periodically and alternately blocks the two exhaust nozzles of the combustion chamber, inducing a large amplitude transverse acoustic modulation. The flame region is then submitted to high amplitude transverse acoustic modes. The Large-Eddy Simulation (LES) flow solver AVBP from CERFACS and IFPEN is used in this work. The solver has been previously extended to handle high-pressure transcritical flows in a collaborative effort carried out by CERFACS and EM2C, CNRS. Results obtained by exploiting high-end computational resources demonstrate the feasibility of such calculations and provide insight in the process. The simulations highlight the mechanisms which can feed energy in the transverse mode and suggest possible descriptions of the driving processes. It is shown that calculations retrieve features found in experiments: the flames are more compact when they are made to interact with the transverse acoustic waves. The dense core length is notably reduced. The flames and dense cores are flattened in the spanwise direction, a feature which is also found in experiments. The unsteady motion observed experimentally is thus well obtained numerically. The transverse motion induced by the acoustic modulation is analyzed in detail. It is found that this motion closely follows the acoustic waves formed in the chamber in good agreement with a model proposed by Mery et al. [1].