This paper presents a numerical study of a uniform flow past a rectangular cylinder using the incompressible lattice Boltzmann method (ILBM). Firstly, we use the ILBM to simulate the flow past a square cylinder symmetrically placed in a two-dimensional channel and results are validated against the well-resolved results obtained using finite-difference method and finite-volume method. Secondly, the effects of the aspect ratio defined as $R$ = width/height on the fluid forces, vortex shedding frequency and the flow structures in the wake are investigated. Aspect ratios ranging from 0.15 to 4.00 and four Reynolds numbers $Re$ = 100, 150, 200 and 250 are selected for the investigation. The results show that the effects of aspect ratio on physical quantities such as drag and lift coefficients, Strouhal number and the vortex shedding mechanism are very notable in the range between 0 and 2. In general, the drag coefficient decreases with the aspect ratio and the decreasing rate is more distinct in the range of $0.15{leq}R{leq}2.0$. There is no local maximum found at around $R$ = 0.6 in the drag coefficient as reported for higher Reynolds numbers in the literature. However the root-mean-square value of the lift coefficient shows a maximum value at $R{approx}0.5$ for all Reynolds numbers selected. The variation of Strouhal number with $R$ appears to be different for four selected Reynolds numbers. Especially for $Re$ = 250, a discontinuity in $St$, as has been observed for higher Reynolds numbers, is observed at around $R$ = 1.45 where multiple peaks are found in the result of Fourier spectrum analysis of the lift force and irregular vortex shedding behavior with no fixed shedding frequency is observed from the instantaneous vorticity contours. Such discontinuity is not observed for $Re$ = 100, 150 and 200. The present results using the LBM are compared with some existing experimental data and numerical studies. The comparison shows that the LBM can capture the characteristics of the bluff body flow well and is a useful tool for bluff body flow studies.