A rarefied gas flow through a slit in an infinite plane wall, induced by a small pressure difference across the slit, is studied on the basis of the kinetic theory. The system of integral equations for the macroscopic variables (the velocity, density, and temperature of the gas), derived from the linearized Boltzmann–Krook–Welander equation with the diffuse reflection boundary condition, is solved by constructing the Neumann series numerically. The flow velocity, density, and temperature fields of the gas as well as the mass flux through the slit are obtained with good accuracy for various Knudsen numbers. The correction to the free molecular flow result for large but finite Knudsen numbers is also obtained analytically, which gives a continuous transition from the free molecular flow to the present numerical result.