A kinetic theory analysis is made of low-speed rarefied gas flows around a flat plate. The Boltzmann equation simplified by a collision model is solved by means of a finite difference approximation with the discrete ordinate method. The method does not suffer from statistical noise which is common in particle based methods and requires much less amount of computational effort. Calculations are made for flows around a micro-scale flat plate with a finite length of 20 microns. The method is assessed by comparing the results with those from several different methods and available experimental data.