A novel model of dark matter (DM), elastically compressible, can contribute to the acceleration of our Universe expansion. While each galaxy compresses its own DM within its gravitation field, the DM bordering neighboring galaxies, far from their centers, is pulled apart. It is shown that, although the DM pressure tends to zero at such locations, the DM compressibility tends to infinity. This allows the DM to expand between galaxies without gravitation hindrance. The model is consistent with the coupled distributions of baryonic and dark matters, with black hole formation at the centers of large galaxies, with galactic flat rotation curves, with a Tully-Fisher relation, and with Milgrom’s MOND relation. Results are discussed.