We present the new results of the two-dimensional numerical experiments on the cross-sectional evolution of a twisted magnetic flux tube rising from the deeper solar convection zone (-20,000 km) to the corona through the surface. The initial depth is ten times deeper than most of previous calculations focusing on the flux emergence from the uppermost convection zone. We find that the evolution is illustrated by the two-step process described below: the initial tube rises due to its buoyancy, subject to aerodynamic drag due to the external flow. Because of the azimuthal component of the magnetic field, the tube maintains its coherency and does not deform to become a vortex roll pair. When the flux tube approaches the photosphere and expands sufficiently, the plasma on the rising tube accumulates to suppress the tube's emergence. Therefore, the flux decelerates and extends horizontally beneath the surface. This new finding owes to our large scale simulation calculating simultaneously the dynamics within the interior as well as above the surface. As the magnetic pressure gradient increases around the surface, magnetic buoyancy instability is triggered locally and, as a result, the flux rises further into the solar corona. We also find that the deceleration occurs at a higher altitude than in our previous experiment using magnetic flux sheets (Toriumi and Yokoyama). By conducting parametric studies, we investigate the conditions for the two-step emergence of the rising flux tube: field strength > 1.5x10^4 G and the twist > 5.0x10^-4 km^-1 at -20,000 km depth. ; Comment: 42 pages, 13 figures, 2 tables, accepted for publication in ApJ. High-resolution figures will appear in the published version