Continuous casting of steel is currently a predominant production method of steel, which is used for more than 95% of the total world steel production. An effort of steelmakers is to cast high-quality steel with a desired structure and with a minimum number of defects, which reduce the productivity. The paper presents our developed GPU-based heat transfer and solidification model for continuous casting, which is coupled with a submodel used for the prediction of the steel micro-structure. The model is implemented in CUDA/C++, which allows for rapid computing on NVIDIA GPUs. The time-dependent temperature distribution calculated by the thermal model is iteratively passed to the submodel for the steel micro-structure prediction. The structural submodel determines the spatially-dependent rates of temperature change in the strand, for which the interdendritic solidification model IDS predicts the micro-structure of steel. The paper presents preliminary simulation results for the steel grade used for pressure vessel plates, which is sensitive to rapid cooling rates.