Abstract: This paper studies the slab stack shuffling (SSS) problem in the slab yard of iron and steel industry. Different from the existing researches, it considers a new practical requirement, the crane capacity limit of each storage area. The problem is formulated into a nonlinear integer programming model through considering the practical constraints with the objective of minimizing the total shuffle number. Based on analysis on its feature, the model is transformed into linear integer programming models under both situations: whether different rolling items can share common candidate slabs or not. Furthermore, several properties are deduced for the problem to decrease the computational complexity of the models. The experiment results show that the optimization method, based on the proposed linear integer programming models, can obtain the optimal solution for practical scaled problems.