  In this paper, we consider unsaturated poroelasticity, i.e., coupled
hydro-mechanical processes in unsaturated porous media, modeled by a non-linear
extension of Biot's quasi-static consolidation model. The coupled,
elliptic-parabolic system of partial differential equations is a simplified
version of the general model for multi-phase flow in deformable porous media
obtained under similar assumptions as usually considered for Richards'
equation. In this work, the existence of a weak solution is established using
regularization techniques, the Galerkin method, and compactness arguments. The
final result holds under non-degeneracy conditions and natural continuity
properties for the non-linearities. The assumptions are demonstrated to be
reasonable in view of geotechnical applications.
