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A model of stationary axisymmetric air motion in the lower layer of a typhoon is expounded and substantiated. The model takes into account air viscosity and compressibility, as well as the Coriolis force and friction against the Earth surface. The model is reduced to a system of three nonlinear differential equations for the horizontal velocity and density of air averaged in the vertical direction. Introducing the function ββ describing the vertical air flux at the top of the layer, the problem is decomposed into the two following ones solved successively: a boundary value problem for the tangential velocity component and a Cauchy problem for air density. After the solution of these problems, the remaining unknowns (the radial velocity component and pressure averaged in the vertical direction) are obtained explicitly. An efficient numerical implementation of the model is performed. The calculation results are in good accordance with observation data. The numerical experiments performed in this work reveal the existence of two maxima in the dependence of air velocity on the distance from the typhoon center in its lower layer. [ABSTRACT FROM AUTHOR]