Bayesian parameter inversion approaches are dependent on the original forward models linking subsurface physical properties to measured data, which usually require a large number of iterations. Fast alternative systems to forward models are commonly employed to make the stochastic inversion problem computationally tractable. This paper compared the effect of the original forward model constructed by the HYDRUS-1D software and two different approximations: the Artificial Neural Network (ANN) alternative system and the Gaussian Process (GP) surrogate system. The model error of the ANN was quantified using a principal component analysis, while the model error of the GP was measured using its own variance. There were two groups of measured pressure head data of undisturbed loess for parameter inversion: one group was obtained from a laboratory soil column infiltration experiment and the other was derived from a field irrigation experiment. Strong correlations between the pressure head values simulated by random posterior samples indicated that the approximate forward models are reliable enough to be included in the Bayesian inversion framework. The approximate forward models significantly improved the inversion efficiency by comparing the observed and the optimized results with a similar accuracy. In conclusion, surrogates can be considered when the forward models are strongly nonlinear and the computational costs are prohibitive.