This paper reports on recent progress in the investigation and modelling of joint effects of compression and swirl on turbulence in a cylinder of a single-stroke rapid compression machine (RCM). Experimental and modelling investigation in a flat cylinder geometry, reported earlier (Hanjalic et al., 1997b), have been extended to cover a 'squish' configuration with a bowl in cylinder head and to broaden the range of operating conditions. In addition, the Direct Numerical Simulations (DNS) of all three operational modes of RCM have been performed: steady rotation and transient spin-down without and with compression. The Reynolds-Averaged Navier-Stokes simulation (RANS) were performed using the low-Re-number second-moment closure. The results obtained are compared with the experimental results (Volkert et al., 1996, 1998) and with DNS (Pascal, 1998). Prior to the computation of the RCM, the applied turbulence model was validated in several generic flows relevant to the RCM: developed and developing flows in an axially rotating pipe, swirling flows in combustion chamber geometries and long straight pipes (Jakirlic et al., 1998), as well as in several compression flow cases, ranging from homogeneous compression to the compression in a closed cylinder. It is demonstrated that in all cases considered the applied RANS model reproduces well both the DNS and experimental results.