Estimating the parameters of advanced soil model is a highly challenging task that requires an in depth understanding of the soil model along with significant human intervention due to the tedious iterative nature of the calibration process. As a result, the parameter calibration becomes time consuming and its outcome varies depending on the user discretion. Among various available inverse analysis methods, the Bayesian approach utilizing Markov chain Monte Carlo (MCMC) simulations has exhibited notable efficacy in determining the constitutive model parameters. In the present study, the potential application of the MCMC method for the parametric identification of a hardening-type elastoplastic soil constitutive model has been explored. In this regard, two algorithms have been employed. The first one is a stress-based single-element MATLAB code that predicts the stress-strain and volumetric response of the soil. The second code employs the Bayesian method facilitating the parameter identification process such that the error in both the stress-strain and volumetric soil response is minimized. In this context, sensitivity analysis of the model parameters has been conducted to identify the most sensitive parameters and subsequently, the MCMC algorithm has been applied to estimate these parameters. Finally, a comparison has been presented between the soil response predicted employing the parameters estimated from the manual iteration and MCMC method by the help of root mean squared error. The results show that the MCMC method is robust and computationally efficient in estimating the constitutive parameters with minimal error.