  Recently it was proved that usual (real) Potts model on a Cayley tree has up
to $2^q-1$ translation-invariant Gibbs measures. This paper is devoted to
description of translation- invariant $p$-adic Gibbs measures (TIpGMs) of the
$p$-adic Potts model. In particular, for the Cayley tree of order two we give
exact number of such measures. Mereover we give criterion of boundedness of
TIpGMs.
