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The shear and the bulk viscosities of the hadron gas at low temperatures arestudied in the model with constant elastic cross sections being relativisticgeneralization of the hard spheres model. One effective radius ${r=0.4 fm}$ ischosen for all elastic collisions. Only elastic collisions are considered whichare supposed to be dominant at temperatures ${T\leq 120-140 MeV}$. Thecalculations are done in the framework of the Boltzmann equation with theBoltzmann statistics distribution functions and the ideal gas equation ofstate. The applicability of these approximations is discussed. It's found thatthe bulk viscosity of the hadron gas is much larger than the bulk viscosity ofthe pion gas while the shear viscosity is found to be less sensitive to themass spectrum of hadrons. The constant cross sections and the Boltzmannstatistics approximation allows one not only to conduct precise numericalcalculations of transport coefficients in the hadron gas but also to obtainsome relatively simple relativistic analytical closed-form expressions. Namely,the correct single-component first-order shear viscosity coefficient is found.The single-component first-order nonequilibrium distribution function, someanalytical results for the binary mixture and expressions for mean collisionrates, mean free paths and times are presented. Comparison with some previouscalculations for the hadron gas and the pion gas is done too. This paper is thefirst step towards calculations with inelastic processes included.

Towards precise calculation of transport coefficients in the hadron gas. The shear and the bulk viscosities