Of late, various constitutive models have been proposed in the literature for the purpose of capturing the various complex physical mechanisms governing the creep behavior of soft soil. However, the more complex the model, the greater the number of associated uncertain parameters it has, and the less robustness it is. In this study, the Bayesian model class selection approach is applied to select the most plausible/suitable model describing the creep behavior of soft soil using laboratory measurements. In total, one elastic plastic (EP) model and eight elastic viscoplastic (EVP) models are investigated. To assess the performance of the different models in the prediction of creep behavior of soft soils, Bayesian model class selection is respectively performed using the oedometer test data from the intact samples of Vanttila clay and reconstituted samples of Hong Kong Marine Clay collected from the literature. All unknown model parameters are identified simultaneously by adopting the transitional Markov Chain Monte Carlo (TMCMC) method, and their uncertainty is quantified through the obtained posterior probability density functions (PDFs). The result shows that the proposed method is an excellent candidate for identifying the most plausible model and its associated parameters for different kinds of soft soils. The approach also provides uncertainty evaluation of the model prediction based on the given data.