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We present an analysis of stability, heating and quench propagation in a 50 Tesla solenoid immersed in a liquid helium bath at 4.2 K, obtained by numerical Finite Element Method (FEM) modeling. The solenoid was assumed to be wound of a cable made of YBCO coated conductor tapes. Full heat transfer curve in the whole temperature range (from 4.2 K up to 300 K) for liquid helium, taken from experiment, was used. An anisotropic continuum model of the winding for thermal propagation, with input data taken from experiments, was developed and adopted in computations. Magnetic field and temperature dependent parameters, such as electrical and thermal conductivities, heat capacities etc., also taken from experiments, were considered. We modeled a single-coil 50 T solenoid as well as a segment approach, in which a 34 T winding, segmented radially, is the inner-most part of a system of and NbTi solenoids providing a background field of 16 Tesla. Stress-strain modeling showed that due to a strong anisotropy of in YBCO film, the critical current of the solenoid is not limited by mechanical forces, but by the radial magnetic field component in the winding, i.e. by the field component parallel to c-axis of YBCO film. We found quite a high degree of stability of the 50 Tesla solenoid with existing stagnant normal zones and significant heat conduction across the winding.