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The problem of rarefied gas flow through a long cylindrical channel as a function of the pressure and the temperature maintained at the channel ends is considered on the basis of the S-model of the Boltzmann kinetic equation. The pressure and temperature drops between the channel ends vary from small values at which the linear transport theory is valid to large values at which the gas molecule mean free path ceases to be constant along the channel. The solution to the model kinetic equation is found by means of the collocation method using the Chebyshev polynomials and rational functions. The mass flow and the pressure in the channel are obtained. Isobaric and isothermal flows are investigated. [ABSTRACT FROM AUTHOR]