Many serious defects in continuous casting of steel, including surface cracks and depressions, are related to thermal-mechanical behavior during solidification in the mold. A finite-element model has been developed to simulate temperature, stress, and shape of the steel shell near the strand surface, as it moves down the mold at the casting speed in a state of generalized plane strain. The thermal model simulates transient heat transfer in the solidifying steel shell and across the interfacial gap between the shell and the mold wall. It is coupled with a stress model that features temperature-, composition-, and phase- dependent thermal-elastic-visco-plastic constitutive behavior of the steel. Depressions are predicted to form when the shell is subjected to either excessive compression or tension, but the shapes differ. Predicted depression shapes are compared with previous plant observations. The model reveals new insights into the mechanisms of surface depressions and longitudinal cracks in this process.