Calculations of the electronic structure demonstrate that band gap modification such as opening and closure is easily achieved by radial deformations perpendicular to the tube axis. Deformations open the gap in metallic armchair tubes only if the mirror symmetries are broken, and further distortions greatly enhance the gap due to new bonds formed between facing layers. Similar deformations increase the gap in small-gap zigzag tubes, but gap closure occurs due to enhanced sigma*-pi* hybridization effects. This band gap modification is crucial at metal contacts and has important implication in fabricating a quantum dot or multiple quantum dots. [S0163-1829(99)13039-X].