Buoyancy-driven motion of an air bubble in a square capillary filled with an immiscible liquid is experimentally studied. When the bulk fluid is Newtonian, the small bubbles are nearly spherical. As the bubble volume increases, the bubbles become prolate with fore and aft symmetry. The terminal velocity also increases as the bubble volume increases. As the bubble size becomes comparable to the capillary size, the terminal velocity reduces and for very large bubble volumes, the bubble velocity is independent of the bubble size. The effect of elasticity in the bulk fluid phase on the buoyancy-driven motion of bubbles is considered. In the presence of elasticity in the bulk phase, a cusp develops at the trailing end of the bubble. The terminal velocity of the bubbles shows multiple maxima as the bubble volume is increased in smaller channels. However, for very large bubbles the terminal velocity again becomes independent of bubble size. The effect of fluid rheology on the bubble shapes and velocity-volume curves is explored.