Low-temperature (at T < 900-950 K) ignition delays of hydrogen-air mixtures are mainly measured in rapid compression machines (RCM). This communication is aimed at numerical simulation of ignition delays of hydrogen-air mixtures in the RCM by means of a coupled three-dimensional (3D) Unsteady Reynolds-Averaged Navier-Stokes (URANS) - Particle Method (PM) simulation of RCM operation capable of catching turbulence-chemistry interaction. The study indicates that the time history of piston motion in an RCM affects the final state of a test mixture at the end of compression stroke and therefore influences the phenomena relevant to test mixture ignition. More specifically, the calculations show that different laws of piston motion at a fixed average piston velocity (i.e., fixed piston displacement and fixed compression time) and fixed compression ratio result in different evolution of mean pressure, temperature and velocity fields in the RCM test section leading to different ignition behavior. The reasons for the arising differences lie in the fact that the local instantaneous piston velocity determines the roll-up vortex structure, strength and turbulence dissipation in it, heat transfer in test-section walls, and mass leakage through piston rings. (C) 2013 Elsevier Ltd. All rights reserved.