The very rapid cooling problem from $820^{circ}$C to $20^{circ}$C on the surface of the steel by thermal conduction including the latent heat of phase transformation of steel and by transient boiling heat transfer of water are considered to principal problem in quenching. The transient boiling process of water at the surface of specimen during the quenching process were experimentally analyzed. Then the heat flux was numerically calculated by the numerical method of inverse heat condition problem. In this report, the simulation program to calculate the cooling curves for large rolls was made using the subcooled transient boiling curve as a boundary condition. By this simulation program, the cooling curves of rolls from D=50mm to D=200mm were calculated and the effects of agitation of circulation of water also investigated.