To investigate different responses of direct and indirect tensile strengths to loading rate, direct and indirect tension tests were performed on sandstone, rust stone, and granite specimens. Typical load curves indicate that a peak tensile stress frequently appears before the second peak stress, used to calculate the tensile strength in indirect tension tests. As expected, increase in the loading rate increases the tensile strength. In addition, the calculated tensile strengths of the indirect tension tests are frequently higher. Interestingly, the increase ratio of the tensile strength with the increase in the loading rate in indirect tension tests is higher. To verify the above results, crack propagation and stress evolution in direct and indirect tension tests were dynamically monitored using PFC 3D. For direct tension tests, specimens fail at the peak tension point, corresponding to the tensile strength. However, for indirect tension tests, minor cracks, composing of continuous microcracks, form before the peak stress and accompany with the decreased slope of the compression curve. At the peak point, tensile stresses significantly concentrate at the crack tips and further cause large-scale crack propagation. In addition, the initiation stress instead of the peak tensile stress is closer to the tensile strength, obtained from the direct tests for the same loading rate.