A model for J/\Psi  suppression at a high energy heavy ion collision is presented. The main (and the only) reason for the suppression is J/\Psi  inelastic scattering within hadron matter. The hadron matter is in the form of an evolving multi-component point-like non-interacting gas. The estimations of the sound velocity in the gas and the approximate pattern of cooling caused by the longitudinal expansion are also presented. It is shown that under such circumstances and with J/\Psi  disintegration in nuclear matter added, J/\Psi  suppression evaluated agrees well with NA38 and NA50 data. Additionally, some rough estimations of J/\Psi  suppression in hadron matter described in the framework of the excluded volume gas model are given.

PACS numbers: 14.40.Lb, 24.10.Pa, 25.75.--q