The effectiveness of a hydraulic fracturing technology has been primarily attributed to a creation of the geometry in the primary fracture. This concept however has been challenged particularly in low-permeability formations in which the size of a Stimulating Reservoir Volume (SRV) becomes the most important issue. Unlike the primary fracture, the area in the SRV is controlled by the fundamental geomechanics behaviors of the formation and a secondary fracture network propagation with possible different modes, and more importantly by the formation permeability change which is controlled by the induced stresses near the primary fracture. In this paper, the induced stresses near a hydraulic fracture in a pure elastic, poroelastic, dual-porosity media are analyzed and compared in order to characterize the low-permeability, sandstone and fractured formations, respectively. The general formulation for a fractured reservoir by a dual porosity model is developed and pore pressures and stresses near a wellbore and a hydraulic fracture are highlighted for production enhancement as the permeability change near a wellbore or a hydraulic fracture may contribute to such an enhancement significantly. Those key parameters controlling the pressure and stresses change and numerical method used are analyzed and presented.