To facilitate industrial vessel lining design for various material properties and lining configurations, a method, being composed of the back-propagation artificial neural network (BP-ANN) with multiple orthogonal arrays, is developed, and a steel ladle from secondary steel metallurgy is chosen for a case study. Ten geometrical and material property variations of this steel ladle lining are selected as inputs for the BP-ANN model. A total of 160 lining configurations nearly evenly distributed within the ten variations space are designed for finite element (FE) simulations in terms of five orthogonal arrays. Leave-One-Out cross validation within various combinations of orthogonal arrays determines 7 nodes in the hidden layer, a minimum ratio of 16 between dataset size and number of input nodes, and a Bayesian regularization training algorithm as the optimal definitions for the BP-ANN model. The thermal and thermomechanical responses of two optimal lining concepts from a previous study using the Taguchi method are predicted with acceptable accuracy.