Geomaterials containing fissures such as some sedimentary rocks often exhibit a bimodal pore size distribution, and they are also inherently anisotropic due to the distinct bedding planes. Hydromechanical modeling of solid deformation and fluid flow of such geomaterials remains a significant challenge. In this paper, we have developed a unique anisotropic double porosity elastoplastic framework to describe such processes. Furthermore, for the solid constitutive model, because of the loss of stress tensor coaxiality between the trial state and the final state, we have derived a new implicit return mapping algorithm to obtain the updated effective stress, history parameters and consistent tangent operator for any given strain increment efficiently, followed by a uniaxial strain point simulation to provide benchmark results. Subsequently, 3D stress point simulations are carried out to calibrate the projection and plasticity parameters using triaxial experimental data as well as to illustrate the strain-softening phenomenon. Initial boundary value problem simulations have been conducted to analyze the impacts of fluid flow and solid constitutive model on the resulting geomaterials’ responses. The overarching goal of this paper is to better understand the coupled solid deformation-fluid flow in the transversely isotropic fissured rocks.