A method predicting the thickness of solid and liquid slag films is presented to understand the complicated heat transfer from the strand to mold for round billet continuous casting. A mathematical model is also developed to calculate the liquid slag lubrication and solid slag friction on the basis of mechanics of viscous fluids and the contact state between the solidifying shell and mold. And a new criterion, based on the nonuniformity of mold heat transfer around the perimeter is proposed to predict the longitudinal crack. The results show that in the upper mold the distribution of the thickness of liquid slag film is similar with that of the solid one, and both of them are nonuniform around the mold perimeter, so does the mold friction. Increasing the casting speed could advance the time of crack formation for one casting process. By comparison, the sensitive area of the longitudinal crack predicted by the new criterion corresponds to that by a stress-based crack criterion. It may lay the theoretical foundation for the on-line detection of billet quality and the visualization of the continuous casting mold process.