This work is dedicated to the numerical simulations of the dynamics of toroidal magnetic flux tubes (MFTs) in the accretion disk of a young T Tauri star. The equations of MFT dynamics take into account the buoyancy and drag forces, the magnetic field of the disk, and the tensions of the internal magnetic field of the MFT. The case of efficient heat exchange with the surrounding gas is considered. The structure of the accretion disk is simulated using the magnetohydrodynamic (MHD) model of the accretion disks developed by Dudorov and Khaibrakhmanov. The equation of state for a polytropic gas is used to model the vertical structure of the disk. Simulations show that MFTs with cross-section radius of 0.1H, where H is the disk scale height, rise almost vertically to the disk surface at a speed of up to 7 km s -1 . Thin MFTs with cross-section radius of 0.001H float up with velocities up to 20 km s -1 and contract towards the axis of rotation. During evolution, MFTs can expand to sizes comparable to the accretion disk scale height and form an inhomogeneous outflowing magnetized disk corona. Floating of MFTs is an effective mechanism for removing excess magnetic flux from the inner regions of the disk, where the ionization fraction is large, and the magnetic field is frozen into gas. The MFT concentration near the disk rotation axis can affect the generation of jet outflows and cause the observed jet inhomogeneities.