Consider a rarefied gas in an infinite two-dimensional channel domain that is periodic horizontally and in the whole space vertically. At the fluid level, the uniform shear flow (USF) is in an inhomogeneous equilibrium state where density and temperature are constant and the vertical velocity is zero, while the horizontal velocity is linear along the vertical direction. At the kinetic level where the gas motion is described by the Boltzmann equation with the finite Knudsen number, the USF is determined by a self-similar non-Maxwellianprofile with an exponentially growing temperature in case of the Maxwell molecules. We construct the unique smooth solution to the USF for any small shear rate, and prove the dynamical stability under small perturbations along the horizontal direction. This work is joint withShuangqianLiu (Central China NormalUniveristy).