Abstract: In this work, the gas-liquid two phase fluid flow and the recirculating flow field in the bottom blown argon stirred bath are studied by means of experiments carried with physical model together with numerical solutions of the mathematical model. The mathematical model consists of the turbulent flow mean vorticity transport equation and stream function equation. K-ε turb-ulance two equation model, the pure buoyance madel and the boundary conditions, The mathematical model is numerically solved implicitly using methed for solving recirculating flow problems developed by prof, Spalding, so that the flow pattern and dislributions of velocity,turbulence kinetic energy, turbulence kinetrc energy dissipation rate, vorticity, the turbulence viscosity, the density and the gas void fraction ratio are obtained. Velocity distribution computed agree well with those measured by laser Doppler anemometer, the computed flow patterns together with the position of the centre of the recirculation flows are in agreement with those obtained by photograpies taking from flow visualization. It shows that, the mathematical model together with its method of solution used arc acceptable for predicting the velocity field in domain of the problem worked, and this work therefore is of practical significamce.