A porohyperelasticÐtransportÐswelling "PHETS# model is presented in which a soft hydrated tissue material is viewed as a continuum composed of an incompressible porous solid " _brous matrix# that is saturated by an incompressible ~uid "water# in which a mobile species "solute# is dissolved[ This PHETS theoretical model is implemented using a _nite element model "FEM# including inherent nonlinearity\ coupled transport processes\ and complicated geometry and boundary conditions associated with soft tissue structures[ The PHETS material properties are clearly identi_ed with a physical basis describing and quantifying elasticity\ permeability\ di}usion\ convection\ and osmotic properties[ The equivalence between the PHETS and the triphasic "TRI# model "Lai et al[\ 0880# is established using the phenomenological equations\ and mathematical expressions are given to relate the PHETS and TRI material properties[ A principle of virtual velocities "PVV# links Eulerian and Lagrangian PHETS formulations and provides correspondence rules between the Eulerian and the Lagrangian _eld variables and material properties[ The PVV is also the basis for a mixed Lagrangian PHETS FEM "Kaufmann\ 0885#\ which was developed for the analysis of soft hydrated tissues[ Selected PHETS FEM results are presented in order to demonstrate the capability of the PHETS model to simulate coupled deformation\ stress\ mobile water ~ux\ and albumin ~ux in the arterial wall undergoing _nite straining associated with pre! ssurization\ axial stretch\ and changes in albumin concentration in bath solutions surrounding a segment of rabbit thoracic aorta[ Values for isotropic material parameters and speci_c details of the experiments and data!reduction methods were obtained from Simon et al[ "0886 ^0887#[ Þ 0887 Elsevier Science Ltd[ All rights reserved