To reveal the characteristics and the evolution of cylinder wakes, two-dimensional flow around a circular cylinder at low Reynolds numbers in finite channel was numerically simulated on the computational fluid dynamics code FLUENT using the multi-block radial girds. The effects of pressure-velocity coupling, pressure discretization, and momentum equation discretization on the computation accuracy were discussed. The results show that the discretization scheme of the momentum equation contributes principally to the formation of errors. The combination of SIMPLEC, second-order pressure discretization, and QUICK is found to be more appropriate for the simulation of the two-dimensional flow around a circular cylinder at low Reynolds numbers in a finite channel. It is also found that the static pressure fluctuates markedly along the channel axis within 2.6-12 times of the channel's width. With the increase of the flow velocity, the position of the maximum pressure drop moves towards the circular cylinder, and the magnitude of the radial static pressure increases.