Fluid　penetration　has　been　observed　to　have　significant　impacts　on　the　distributions　of　pore　pressure　and　effective　stress　in　hydraulic　fracturing　experiments.　This　fluid　penetration　is　usually　simulated　by　the　invariable　boundary　method　which　neglects　the　impacts　of　fluid　front　motion　and　introduces　significant　errors　in　the　simulation　of　hydraulic　fracturing.　This　study　proposed　a　moving　boundary　method　to　describe　the　fluid　front　motion　and　established　an　anisotropic　fluid-solid-motion　coupling　model　for　fluid　penetration　into　anisotropic　porous　media.　The　performances　of　invariable　and　moving　boundary　methods　were　numerically　evaluated　for　the　impacts　of　fluid　front　motion　on　the　field　variables　(including　pore　pressure,　principal　stresses　and　permeability)　and　breakdown　pressure.　Simulation　results　showed　that　the　penetration　depth　and　pore　pressure　distribution　obtained　from　the　moving　boundary　method　fit　experimental　observations　better　than　those　obtained　from　the　invariable　boundary　method.　Anisotropic　fluid　front　motion　forms　a　changing　elliptical　seepage　zone.　The　pore　pressure,　principal　stresses,　hoop　and　radial　permeability　have　significant　changes　within　seepage　zone.　The　fluid　front　is　the　dividing　line　between　seepage　zone　and　initial　state　zone.　The　moving　boundary　method　can　accurately　simulate　the　hydraulic　fracturing.　©　2020　Elsevier　Ltd