This paper involves the study of the statistical solution of the BGK equation of two simple viscous fluid flow problems: flow over a at plate and a planar Couette flow. Both of the problems have been studied using DSMC method and the statistical solution of the BGK and ES-BGK equations. The first problem involves supersonic flow (M=3) of argon gas over a at plate assuming adiabatic and isothermal boundary conditions and the second problem of planar Couette flow problem involves a gas confined between two parallel plates moving relative to each other. These types of flows are commonly found in microuidic applications. For both of the problems, the BGK and ES-BGK solutions are compared with the exact, well known DSMC method as well as theoretical solutions that include velocity slip and temperature jump boundary conditions. It was found that the solutions obtained by the statistical BGK and ES-BGK methods agree well with the theoretical and the benchmark DSMC solutions. In addition, the statistical BGK and ES-BGK methods are shown to be numerically more efficient than the DSMC method. For both of the problems, the statistical ES-BGK solutions are shown to be in better agreement with the analytical and the benchmark DSMC solutions than the BGK ones. For the planar Couette flow problem, it will be shown that a theoretical solution for incompressible, argon, transitional ow (Knudsen number = 0.01) remains valid beyond the applicability ranges suggested in the original work.