The mode II fracture toughness and strength due to shear stress are important parameters in the stability of caprock and injection zone with application to geological sequestration of carbon dioxide. In this research, a short beam compression test has been used to determine the shear strength and the mode II fracture toughness for Coconino sandstone. The average value of the shear strength and mode II fracture toughness are estimated to be 23.53 MPa and 1.58 MPa${surd}$m respectively. The stress intensity factor is suggested by finite element analysis using the displacement extrapolation method. The effect of biaxial stress and water saturation on the fracture toughness has also been investigated. The fracture toughness increases with confining stresses, but decreases by 11.4% in fully saturated condition.