Solid deformation is always a crucial factor in the shale gas transport model. While previous studies always adopt the assumption of isotropic poroelastic deformation, anisotropic poroelastoplastic deformation is rarely considered, despite the anisotropy being a ubiquitous property of natural rocks. In this work, an anisotropic poromechanical model is established to analyze the matrix porosity and apparent permeability evolutions during the process of shale gas migration. A novel feature of the model is the use of the mixture theory and Biot tensor to derive a rate form for matrix porosity. Subsequent backward integration gives matrix porosity an explicit expression, which can be further substituted into several sophisticated apparent permeability models for full-scale analysis. A recently developed constitutive model appropriate for rocks exhibiting transverse isotropy in both the elastic and plastic responses is adopted in this work. Through the stress point simulation of Terzaghi effective stress and alternative strain tensors, a new ``double-U'' shape curve of apparent permeability is obtained, which cannot be reproduced from the assumption of isotropic poroelasticity. Parametric studies of some plasticity and adsorption parameters are also performed. Finally, a three-dimensional and a plane strain initial-boundary value problems are conducted, from which the impacts of anisotropic poromechanics (Biot tensor, Ev/Eh ratio, bedding plane orientation) on gas production, stress distribution, and equivalent plastic strain are revealed. Advice on the proper use of the simplified gas production model is also provided.