A reliable geological cross-section is essential to the design and risk assessment of underground structures. Random fields are commonly employed to model geological uncertainty. However, determining the covariance parameters can be a challenging task. In this study, a Bayesian approach is introduced for the simulation of geological formations utilizing available boreholes from a specific site. The cross-section and its associated covariance parameters are learned from geological formations observed in boreholes, using the Markov Chain Monte Carlo-based Bayesian method. A cross-section consisting of seven boreholes in Botanic Gardens, Singapore is used to demonstrate the effectiveness of the proposed method. The results show that the stochastic simulation of geological formations has a sound performance. For the training boreholes, most geological formations have true positive rates and positive predictive values larger than 0.89. For the validation boreholes, almost all geological formations in boreholes are accurately identified. When plenty of boreholes are available, a uniform prior distribution is a better choice to reduce geological uncertainty. Alternatively, when borehole data is limited, a log-normal prior distribution can be used to ensure a more deterministic simulation. For a length of 300-m cross-section of four ordered geological formations, when the number of boreholes is greater than three, the posterior standard deviation of the geological model is less than 10% of the prior, and the effective range of a single borehole is found to be between 21 and 27 m.