Proper definition of certain material properties is a paramount issue for accurate simulation. However, the values of a material parameter are commonly uncertain due to multiple factors in practice. To obtain reliable material parameters, parameter identification via Bayesian theory has become an attractive framework and received more attention recently. Based on this frame, the determination of likelihood function is critical for posterior probability. Unfortunately, it is commonly difficult to be determined directly, especially for complex engineering problems. In this study, Bayesian formulas for material parameter identification are given. To make it feasible for real engineering problems, the least square-support vector regression surrogate and Monte Carlo Simulation are integrated to obtain the maximum likelihood estimation of likelihood function. The uncertainty of parameter identification is quantified via the Bayesian method. In two benchmarks, two cases with single and multiple uncertainty sources are used to propagate and quantify uncertainties in material parameters based on Bayesian approach. Moreover, the proposed method is used to identify the material parameters of advanced high strength steel used in vehicle successfully.