Development of a supercritical geothermal system at great depth has been proposed to enhance geothermal heat extraction. Hydraulic fracturing at great depth may induce mixed-mode (opening and shear mode) crack propagation due to high tectonic stress. The purpose of this study is to predict the crack growth behavior under high tectonic stress conditions corresponding to great depth. This study presents a finite element model for the analysis of hydraulic fracturing, taking mixed-mode fracture into account. In the finite element model, an embedded crack element is employed to represent arbitrary crack geometry due to mixed-mode crack propagation. A mixed-mode failure criterion, including a fracture process zone model, is incorporated into the embedded crack model as a crack constitutive law. The growth behavior of hydraulically induced cracks is analyzed.