Multiphase transport in unsaturated swelling porous materials involves fluid mass transport, heat transfer as well as swelling of the porous solid matrix. Neglecting the deformation of the solid matrix can lead to erroneous results when modeling transport phenomena in porous materials. In particular, many porous materials exhibit viscoelastic effect upon wetting/drying, which can expedite or slow the transport process. This work presents modeling and simulation of two-way coupling of multiphase transport and viscoelastic large deformation of unsaturated swelling porous systems based on fundamental physics. The work includes the development of a thermomechanical theory for multiphase transport in unsaturated swelling porous media based on the Hybrid Mixture Theory (saturated systems can also be modeled as a special case of this general theory). The theory includes three phases: solid matrix, fluid and air and uses the Coleman-Noll procedure to obtain restrictions on the form of the constitutive equations. Derived relationships include, for example, a modified Darcy's law, which takes into account both Fickian and non-Fickian transport, and a viscoelastic constitutive relationship that relates the stress and strain tensors for the solid phase. A model is then developed based on this theory for isothermal conditions which involves a simple form of a differential-integral equation that governs the fluid transport and is fully coupled with the solid large deformation. Numerical implementation of this model is then presented that involves a finite element analysis of water absorption of plane sheet pasta and numerical results of sorption curves show good agreement with experimental results obtained from the literature. Importance of including viscoelastic relaxation is investigated for soaking processes of pasta. Drying of potato is also considered in this work as an important example of two-way coupling of multiphase transport and viscoelastic large deformation of the solid matrix of porous materials because during drying processes, the transition of outer surface of the material from rubbery to glassy state at low moisture content can slow or stop shrinkage of the materials, and thus viscoelasticity plays an important role.