Strength and fracture toughness of rocks are important parameters in various fields of rock engineering application. Many researchers have reported that strength and fracture toughness of rocks increase with loading rate. The loading rate is related to time-dependent behaviors of rocks and it important factor for assessing long-term stability of underground structures. In this study, Brazilian tension tests for tensile strength and short beam compression tests for shear strength were carried out with different loading rates ranging from 0.01 MPa/s to 10 MPa/s using Coconino sandstone. Similarly, mode I, mode II, mode III fracture toughness tests were performed with the same loading rate of strength tests. Grooved disc specimens, short beam compression specimen, and circumferentially notched cylindrical specimens were employed for fracture toughness tests. The results show that both rock strength and fracture toughness are proportional to 1/(n+1) th power of loading rate, where the parameter n represent subcritical crack growth due to stress corrosion. The values of n are almost constant regardless of loading configuration. Also, literature reviews show that the values of n are different form rock types. Thus, the parameter n can be considered a material constant of rocks.