Steel strip feeding into continuous casting mold is an innovative technology improving the slab quality through decreasing the melt superheat and increasing the proportion of equiaxed dendrites. To investigate the embedded complex melting and solidification processes, a mathematical model has been developed to model all the essential physical behaviors of the fluid flow, heat transfer, melting, and solidification during steel strip feeding into the mold. The enthalpy method is adopted to describe both the melting of steel strip and the solidification of slab. The complex heat transfer between cold steel strip and hot melt is considered. The melting of moving strip and the growth of solidified shell are compared with the experimental measurements and empirical equation, respectively. The validated model is then used to predict the melting and solidification characteristics during steel strip feeding into the mold. Based on the experimental and numerical findings, the whole melting process of steel strip can be divided into three periods: the steel sheath formation, steel sheath melting, and steel strip melting. Effects of the strip thickness (), melt superheat (), and strip feeding speed () on the melting of steel strip have been analyzed. An empirical equation is proposed to correlate the total melting time with aforementioned parameters: . Furthermore, sensitivity study has also performed to reveal the influence of the strip thickness, melt superheat, and strip feeding speed on the final strip tip position.