Parameter identification using Bayesian approach with Markov Chain Monte Carlo (MCMC) has been verified only for certain conventional simple constitutive models up to now. This paper presents an enhanced version of the differential evolution transitional MCMC (DE-TMCMC) method and a competitive Bayesian parameter identification approach for applying to advanced soil models. To realize the intended computational savings, a parallel computing implementation of DE-TMCMC is achieved using the single program/multiple data technique in MATLAB. To verify its robustness and effectiveness, synthetic numerical tests with/without noise and real laboratory tests are used for identifying the parameters of a critical state-based sand model based on multiple independent calculations. The original TMCMC is also used for comparison to highlight that DE-TMCMC is highly robust and effective in identifying the parameters of advanced sand models. Finally, the proposed parameter identification using DE-TMCMC is applied to identify parameters of an elasto-viscoplastic model from two in situ pressuremeter tests. All results demonstrate the excellent ability of the enhanced Bayesian parameter identification approach on identifying parameters of advanced soil models from both laboratory and in situ tests.