We study the phenomenon of high energy proton stopping in the nuclear matter and suggest theeffective model that describes this effect. To compare our model with the data of relatively lowenergy experiment [1] we use the correlation between mean multiplicity and number of so-calledgrey nucleons - particles, which are knocked out of the nucleus by the incoming proton.Proton decelerates in the nuclear matter transferring its energy to the production of new particlesin inelastic interactions. We introduce the stopping force from hydrodynamics to explain this de-celeration in an effective way. The idea is to treat target nuclei as a liquid drop with given internalenergy density and volume. As soon as the projectile-proton gets into the target-nuclei the stoppingforce begins to act on it. With this force we obtain a differential equation that describes relativisticmotion of a proton in a nucleus. Setting the final speed - the speed after which binary collisionsdo not contribute to multiplicity - we calculate the length of the proton’s path in the nucleus. Thispath length cuts out a region, in the nucleus to which we apply the Glauber-like approach to obtainnumber of binary collisions. (Note that in a pure Glauber approach, the integration extends to theentire space.) The method of calculating dependency of mean multiplicity on impact parameter isalso suggested. As an input in this model we use empirical dependency of mean multiplicity onenergy in pp-collisions [2] and values ofσNNinel[3].Results on the correlation between mean multiplicity and a number of grey nucleons are comparedin this work to the available experimental data on centrality dependence of stopping andπ−pro-duction in p-Au collisions at a beam momentum of 18 GeV/c[1]. The linear dependence of thecorrelation between mean multiplicity and grey nucleons predicted by the model is well in line withthe experimental data obtained at low numbers of grey nucleons. At the same time, it is shownthat the limited acceptance of pion registration can produce a strong deviation from the linearityas observed in the experiment with slow protons at large values of pion multiplicity and number ofgrey nucleons.Acknowledgments: the reported study was supported by RFBR, research project No. 18-02-40097References:1. I. Chemakinet al., Phys. Rev. C60, 024902 (1999).2. W. Thome ,et al.], Nuclear Physics B129, 365 (1977).3. P.A. Zylaet al.(Particle Data Group), Prog. Theor. Exp. Phys.2020(8), 083C01 (2020)