A numerical study is conducted on the flow characteristics of a rectangular cylinder (chord-to-width ratio C/W= 2-10) mounted close to a rigid wall at gap-to-width ratio G/W= 0.25-6.25. The effects of G/W and C/W on the Strouhal number, vortex structure, and time-mean drag and lift forces are examined. The results reveal that both G/W and C/W have strong influences on vortex structure and shear layer instabilities, which significantly affect the forces on the cylinder. An increase in G/W leads to four different flow regimes, namely no vortex street flow (G/W< 0.75), single-row vortex street flow (0.75≤ G/W≤ 1.25), inverted two-row vortex street flow (1.25< G/W≤ 2.5), and two-row vortex street flow (G/W> 2.5). Both Strouhal number and time-mean drag are more sensitive to C/W than to G/W. For a given G/W, Strouhal number grows with C/W while time-mean drag decays with C/W, the growth and decay being large between C/W= 2 and 4. The time-mean drag is largest in the single-row vortex street regime, contributed by a large pressure on the front surface, regardless of C/W. A higher C/W, in general, leads to a higher time-mean lift. Maximum time-mean lift occurs for C/W= 10 at G/W= 0.75, while minimum time-mean lift appears for C/W= 2 at the same G/W. The impact of C/W on time-mean lift is more substantial in single-row vortex regime. The effect of G/W on time-mean lift is larger at a larger C/W.