Random field theory is often used to model spatial variability of geo-material boundary and property. The results of random field generation based on different theories are quite different; however, few studies discuss the effects of adopting different random field approaches on the established stratigraphic models and their influence on engineering analysis. This article compares two random field approaches for evaluating liquefaction potential at a selected site. Here, based on the results of cone penetration tests (CPTs) at the study site, stratigraphic models are constructed using a continuous random field (conditional random field, CRF) and a discontinuous random field (Markov random field, MRF). Note that the MRF parameters were calibrated with the statistical parameters used in CRF. A series of geological profiles representing realizations of the derived CRF-based and MRF-based stratigraphic models are generated. Then, the liquefaction potential index (LPI) is calculated using the simplified procedure with a simulated geological profile and associated soil parameters. Finally, by repeating the analysis for all realizations of random stratigraphic models, the mean and the coefficient of variation of LPI are determined. Meanwhile, the uncertainty of stratigraphic models generated by CRF and MRF approaches is quantified and expressed as information entropy. Next, the relationship between stratigraphic model uncertainty (as an entropy) and LPI variation (or uncertainty) is established. The results show that: (1) the generation of the stratigraphic model is affected by the chosen random field approach, and the distribution of MRF-based strata is more continuous compared with that of CRF-based strata; (2) due to this effect, the strata uncertainty of CRF simulation is more uniform compared with that of MRF; (3) the information entropy and LPI uncertainty obtained using CRF exhibit moderate correlation, while these parameters obtained using MRF exhibit a strong positive correlation.