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In this article, rarefied gas flow was investigated and analyzed by the Fokker-Planck approach in different Knudsen numbers and Mach numbers at subsonic and supersonic regimes. The presented Fokker-Planck approach is used to solve the rarefied gas flows in different sheardriven micro/nano geometries like one-dimensional Couette flow and the two-dimensional cavity problem. Boltzmann’s equation, and especially statistical technique of the Direct Simulation Monte Carlo (DSMC), are precise tools for simulating non-equilibrium flows. However, as the Knudsen number becomes small, the computational costs of the DSMC are greatly increased. In order to cope with this challenge, the Fokker-Planck approximation of the Boltzmann equation is considered in this article. The developed code replaces the molecular collisions in DSMC with a set of continuous stochastic differential equations. In this study, the Fokker-Planck method was evaluated in the Couette flow in the subsonic Mach number of 0.16 (wall velocity was 50 m/s) and in the supersonic Mach number of 3.1 (wall velocity was 1000 m/s), where Knudsen numbers range from 0.005-0.3. Also, the cavity flow with a wall Mach number of 0.93 (wall velocity was 300 m/s) in Knudsen numbers ranging from 0.05-20 was investigated. The results show that by increasing speed and Knudsen numbers, the accuracy of Fokker-Planck increases. In addition, despite using larger number of simulator particles, the rapid convergence and lower computational costs relative to other methods are the features of this method. [ABSTRACT FROM AUTHOR]