This paper deals theoretically with the stagnation-point flow of a rarefied gas. Representative Mach number M S taken in the continuum flow region is assumed to be small and thus the analysis is based on the linearized B-G-K equation. A method of solution is developed in which the continuum flow and the Knudsen layer flow are considered successively. Actual analysis has been put forward to the second approximation correct to the order of \(\sqrt{M_{S}}\). The phenomena of flow slip and temperature jump at the wall are studied in detail. Numerical discussions are also made of the distributions of flow velocity, density and temperature in the Knudsen layer.