A soft hydrated tissue structure can be viewed as a “PETS” (poroelastic-transport-swelling) model, i.e., as a continuum composed of an incompressible porous solid (fibrous matrix with fixed charge density, FCD) that is saturated by a mobile incompressible fluid (water) containing mobile positively (p) and negatively (m) charged species. Previously, we described two PETS models — a “semi-mixed” porohyperelastic PHETS model (Simon et al. 1998) and a “fully mixed” MPHETS model (Simon et al. 1999) using FEMs (finite element models) that included geometric and material nonlinearity and coupled electrical/chemical/mechanical transport of the fluid and charged species. Here, we demonstrate the equivalence of the PHETS and MPHETS formulations that are useful when the solid and fluid materials are incompressible and the electrical-chemical potential and mechanical-osmotic pressure fields are discontinuous at material interfaces.