The Bhatnagar-Gross-Krook (BGK) model of the Boltzmann kinetic equation for the problem of thermal slip of a rarefied gas along a solid flat surface \[ v_x\dfrac{\partial f}{\partial x'}+v_z\dfrac{\partial f}{\partial z'}=\dfrac{p}{\eta_g}(f_{\mathrm{eq}}-f), \] where \(f(r',v)\) is the desired distribution function of gas molecules on the coordinates and velocities, \(f_{\mathrm{eq}}(r',v)\) is the locally equilibrium distribution function, \(p\) and \(\eta\) are the pressure and dynamic viscosity, respectively, is considered. Its analytical solution is constructed. The distribution of gas velocity and heat flux vector in the Knudsen layer are calculated analytically. It is shown that the results coincide with analogs within the BGK model.