The optimization of refractory linings is a complex task due to the many factors that influence the thermomechanical behavior. This study applies the multiparameter optimization method technique for order preference by similarity to the ideal solution to a commercially used slag zone lining of a secondary metallurgical steel ladle, considering the influence of different material models in a finite element (FE) simulation. The dataset is acquired by varying the working lining brick shape, initial expansion allowance (IEA), and isolation layer thickness. The maximum irreversible strain, joint opening at the hot face, and steel shell temperature are determined from the FE simulation results and used as the input values for the optimization. A larger circumferential brick dimension combined with low IEA is favorable for the von Mises creep model. The main contribution is from the IEA (98.53%). The optimized lining for the Drucker–Prager criterion has a brick with a small circumferential dimension and larger IEA. The main influencing factor is the brick shape (85.06%). The differences in the optimization results and factor contributions can be explained by the contribution of the constitutive models to the simulation results before and after the thermal shock.