In 1993, at the Superconductivity Research Laboratory (SRL), International Superconductivity Technology Centre (ISTEC), in Tokyo, continuous growth of large single crystals of YBa2Cu3O7-x (Y123) was achived by application of Czochralski method. This paper presents the three-dimensional numerical computations of the How and thermal fields in the Ba-Cu-O melt for Y123 single crystal growth by this method. The finite volume method was used to calculate the fluid flow and heat transfer with staggered numerical grid. The flow in the melt was modelled as an incompressible Newtonia and Boussinesque fluid. Calculations are presented for a combined flow regime of buoyancy-driven natural convection and crystal-rotation-driven forced convection.