A mathematical model has been developed to analyze the circulating flow characteristics in RH Degassing vessel designed for two-and multi-legs system. The homogeneous model with the spatially variable density was used to simulate gas-liquid flow in up-legs. The difference of density between pure liquid and gas-liquid was considered to be a driving force of circulation flow. The volume fraction of gas was obtained by modifying the gas plume model of the stirred ladle. The complicated geometry including ladle, vacuum, up-legs, and down-leg was considered by incorporation of blockage technique. Numerical calculations of the circulating flow have been conducted for the water model of RH degassing vessel with twoand multi-legs with changing the air flowrates from 5 to 35 l/min. Computed velocities at the exit of downleg agree well with the observed data available in the literature. The momentum transport in RH degassing vessel with multi-legs will be larger than that with two-legs. This is justified based on fact that the velocities in RH degassing vessel with multi- legs tend to be uniform, i.e. the mean velocity of bulk in a ladle is remarkably larger than that in two-legs. Simulated transient concentration profile of the tracer from top surface to interior shows clearly the difference of flow characteristics between two-and multi-legs RH degassing vessels.