Non-linear calculations of the free-boundary mode in a cylindrical tokamak plasma with finite conductivity are carried out by using the 'pseudo-vacuum' model. Applicability of the pseudo-vacuum model to the study of free-boundary kink modes is carefully checked by linear analysis both analytically and numerically. In the non-linear calculations, vacuum bubbles can be formed due to surface tearing mode as well as to free-boundary kink mode under the condition that the safety factor at the plasma surface, qa, is around two. This bubble formation is a candidate for major disruptions in tokamak discharges with qa approximately equal to two.