The role of gas compressibility in flame acceleration in channels with obstacles is studied analytically. The theory is consistent with the mechanism of extremely fast flame acceleration in obstructed channels obtained recently by Bychkov et al. [Bychkov et al., Phys. Rev. Lett. 101 (2008) 164501]. The present theory accounts for small but finite gas compressibility through expansion for small initial Mach number up to the first-order terms. It is demonstrated that flame-generated compression waves moderate the acceleration process noticeably, and that, for finite but small gas compression, the theory is in good quantitative agreement with numerical simulations. (C) 2010 The Combustion Institute. Published by Elsevier Inc. All rights reserved.