AbstractData-driven material models can capture the constitutive relationship directly from the data without involving any material-dependent mathematical expressions. But most data-driven approaches, such as artificial neural networks, only estimate the deterministic relations and do not consider the material uncertainty. In this paper, the constitutive relation is taken as a stochastic function following the Gaussian process, where a probability-based nonparametric method, called Gaussian process regression (GPR), is used to capture the constitutive relation with the uncertainty being included. Both one-dimensional (1D) and two-dimensional (2D) material data are used to validate the GPR-based constitutive model (GPR model). The obtained GPR model shows higher accuracy than other data-driven approaches, particularly when the data set size is small. When compared with the assumed true model, the GPR-based model has an average relative error of <2.3%. Finally, with the help of the material uncertainty identified by the GPR-based model from the material data, a data-driven stochastic structural analysis procedure is developed. The relative errors of the expected deflection and probability of failure given by the GPR model are smaller than 2% and 3%, respectively.