The nonlinear development of the kink instability of a magnetic flux tube initially lying in mechanical equilibrium in the deep convection zone is presented. The unstable evolution is started by a small-amplitude sinusoidal perturbation of the shape of the flux tube in a vertical plane. As a result of the development of the instability, the lower part of the flux tube enters the radiative core and remains there confined within a fraction of the uppermost pressure scale-height of this region. The rising part of the flux tube crosses the convection zone in a dynamic time-scale of several weeks to a few months, and reaches the photosphere. A numerical code which calculates the dynamic evolution of a thin magnetic flux tube in the convection zone was developed. The code is lagrangian and allows for the compressibility of matter in the flux tube; for convection zone stratification the Spruit (1977) model is used.