Abstract
We consider a Fermi gas of free tachyons as a continuous medium and find whether it satisfies the causality condition. There is no stable tachyon matter with the particle density below critical value ${n}_{T}$ and the Fermi momentum ${k}_{F}<\sqrt{\frac{3}{2}}m$ that depends on the tachyon mass $m$. The pressure $P$ and energy density $E$ cannot be arbitrary small, but the situation $P>E$ is not forbidden. Existence of shock waves in tachyon gas is also discussed. At low density ${n}_{T}<n<3.45{n}_{T}$ the tachyon matter remains stable but no shock wave survives.
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