The　numerical　solution　of　two-dimensional　unsaturated　flow　problems　based　on　the　novel　advanced　computational　meshless　method　was　investigated.　The　numerical　solution　was　approximated　by　superpositioning　the　Trefftz　basis　functions　formulated　from　independent　functions　satisfying　the　governing　equation　in　the　cartesian　coordinate　system.　To　solve　the　two-dimensional　unsaturated　flow　problems,　this　study　adopted　a　linear　approximation　for　the　nonlinear　Richards　equation　to　model　flow　in　unsaturated　soils　using　the　Gardner　exponential　model.　The　validity　of　the　proposed　method　is　established　in　several　problems.　Results　indicate　that　the　proposed　method　may　obtain　highly　accurate　numerical　solution　for　two-dimensional　unsaturated　flow　problems.　Copyright　©　2018　by　the　International　Society　of　Offshore　and　Polar　Engineers　(ISOPE).