Hadron scattering at large and small distances is simultaneously descr
ibed in the framework of the unitarization method based on a generaliz
ed reaction matrix. The assumed dynamics of hadron interactions is ins
pired by the ideas of the chiral quark models. The proposed model for
hadron interactions is based on geometrical notions of the interaction
s of constituent quarks similar to those used by Chou and Yang for the
description of hadronic interactions. This model allows us to reprodu
ce the ln2 s growth of the total cross sections as well as regularitie
s in the behavior of differential cross sections, in particular, its p
ower-law falloff at fixed angles. It also allows us to get the correct
values for the total cross-section ratios of hyperon-proton and proto
n-proton interactions and to estimate the total cross-section values f
or interactions of the hadrons containing heavy quarks.