Integrated Materials and Products Design (IMPD) is a new system-based design approach. This emerging method focuses on designing a product and its materials at the same time to further enhance product performances. In the process of IMPD, material models that predict material properties with given inputs of material processing parameters play an important role in numerous design optimization iteration loops. In this work, a material model for predicting the tensile strength of austenitic stainless steels is developed based on the neural network with Bayesian framework. Using the Bayesian framework, we quantify the degree of uncertainty, originated from lack of data or the architecture of employed neural network, in the prediction of material properties. This quantification is very important for the later use in robust design optimization. Developed material model is validated based on the two different types of austenitic stainless steels, AISI 316L and AISI 347H, subjected to prior heat treatment processes. Comparing the predicted results with experimental results, we observe our material model predicts the tensile strengths of AISI 316L steels heat-treated at various temperatures with higher levels of accuracy. The predicted tensile strengths of AISI 347H steels tested at different temperatures are reasonably close to the experimental results.