In the present study, a rarefied gas flow behavior is investigated numerically using two different approaches. A rarefied gas flow is considered within a double-sided lid-driven cavity which the upper and lower walls are moving in the same direction. As a macroscopic description, the set equations of Navier-Stockes and Fourier (NSF) are resolved numerically. The Monte Carlo simulation (DSMC) method is used as a kinetic based approach to capture the non-equilibrium effects. The flow properties are determined using both approaches as a function of the Knudsen number which estimates the gas flow rarefaction degree.