In this paper, the fluid flow behavior past a pair of rectangular cylinders placed in a two dimensional horizontal channel has been investigated using Lattice-Boltzmann Method(LBM). The LBM has built up on the D2Q9 model and the single relaxation time method called the Lattice-BGK(Bhatnagar-Gross-Krook)model. Streamlines, velocity, vorticity and pressure contours are provided to analyze the important characteristics of the flow field for a wide range of non dimensional parameters that present in our simulation. Special attention is paid to the effect of spacing(d) between two cylinders and the blockage ratio A(=h/H), where H is the channel height and h is the rectangular cylinder height. for different Reynolds numbers. The first cylinder is called upstream cylinder and the second one as downstream cylinder. The downstream fluid flow fields have been more influenced by its blockage ratios(A) and Reynolds numbers(Re) whereas the upstream flow patterns(in front of downstream cylinder) by the gap length(d) between two cylinders. Moreover, it is observed that after a certain gap, both upstream and downstream flow patterns are almost similar size and shape. The simulation result has been compared with analytical solution and it is found to be in excellent agreement.