The uniformity of strand solidification and lubrication in continuous casting mold has a great effect on the slab quality and production stability. In this work, an inverse problem model, based on online measured mold temperature, was developed to simulate mold heat transfer and strand solidification. Through quantifying the local heat flux and its distribution between the mold and strand shell, the temperature field and strand solidified behavior inside mold were obtained. Following Newton law of viscosity, Coulomb law of friction and mixed lubrication theory, the mathematical model of mold flux lubricated and frictional behavior was proposed in view of various contact states between mold flux and strand surface. The non-uniform distributions of slag film thickness, lubrication status and frictional stress were further investigated. The inverse problem model could reflect the non-uniformity of solidification and lubrication, and therefore would provide a worthwhile calculation method for exploring the complex lubricated and frictional behavior inside mold.