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.