Crack initiation and propagation in solid under water pressure is called hydraulic fracturing. Hydraulic fracturing technology has been extensively applied in engineering, including the measurement of in situ stresses [1], stimulation of groundwater wells [2], and solid waste disposal [3]. The hydraulic fracturing mechanism has been extensively studied to improve the hydraulic fracturing design for engineering applications and avoid hydraulic fracturing for engineering safety. The literature shows that the orientation of new fractures is influenced by several factors, such as local stress field [4], geometry of existing fractures [5-6], anisotropy of the rock [7], and ratio between vertical load and hydraulic pressure [8]. However, the propagation direction of newly created fractures and the failure mechanism remain unclear. Numerous laboratory experiments under uniaxial and biaxial loading conditions [7, 9], have been performed to gain insights into fracturing mechanisms. Numerical methods are generally suitable for the examination of rock fracturing behaviors with general geometries and loading conditions. The finite element method (FEM) [8, 10], XFEM [11, 12], RFPA [13], PFC [14, 15], DDA [16], NMM [17], BEM [18], and other methods [19, 20] have been adopted to investigate the fracturing mechanisms in rocks. However, systematic studies on vertical load and hydraulic pressure in existing flaws under different tectonic stresses are limited. In the present article we carried out an in-depth investigation of the effects of hydraulic pressure and tectonic stress on fracture initiation in rock flaws by numerical simulation. The maximum principal stress and maximum shear stress along the flaw perimeter, which are related to fracture initiation, were evaluated.