Steady evaporating flows from a cylindrical condensed phase in an infinite expanse of its vapor gas are investigated numerically on the basis of the Boltzmann–Krook–Welander equation. Not only the mass flow rate and the energy flow rate from the cylinder, but also the local variables of the gas over the whole flow field are obtained for a wide range of the Knudsen number and the pressure ratio, which is defined by the pressure at infinity divided by the saturation gas pressure at the temperature of the condensed phase. The acceleration of gas flows, especially to a supersonic flow, near the cylinder and the deceleration to the stationary state at infinity are clarified. The discontinuity of the velocity distribution function in the gas, a typical behavior of a gas around a convex body, is analyzed accurately with the difference scheme devised for this purpose, and its relation to the *S* layer [Phys. Fluids **1****6**, 1422 (1973)] is discussed.

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*y*for $x\u226b1$ is obtained more efficiently by the equation for $y\xaf(\u2009=\u2009y\u22121/x),\u2009dy\xaf/dx+3y\xaf/x\u2009=\u20090,$ than by Eq. $(*)$ [e.g., solve Eq. $(*)$ for $x\u2a7e10$ under $y(10)\u2009=\u20091].$

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