In order to determine rock tensile strength in a precise way to minimize the negative impacts of the compliance of the drilling-rod hydraulic fracturing system on the determination of the maximum horizontal principal stress, the multiple-diameter core hydraulic fracturing machine to test tensile strengths of rock cores was developed and manufactured. Based on the hydraulic fracturing process and the thick rock cylinder model in rock mechanics，the test machine includes three major parts：load applying system，pressure monitoring and data acquisition system，specimen holding system. In order to make the test machine and the test method widely accepted and used，57 rock sample tests were conducted with respect to the major influential factors，such as pressurization rate，depth and diameter of central blind hole，ratio of internal to external diameters of hollow rock cylinder. The test results show the depths of internal blind holes do not affect the test results significantly，but can lower the success rate of tests，therefore，it is suggested that the depth of internal blind hole should be 0.7–0.8 times of the total height of rock specimen. The test results also indicate that the diameters of internal holes can affect the test results significantly，and the scale effect does not work effectively when the diameter of internal borehole is greater than 20 mm. Considering the ratio between the internal diameter of internal blind hole and the external diameter of rock specimen，it is suggested to adopt 0.3–0.5 to obtain more stable test results according to the theoretical analysis and test results. The adopted test pressurization rate was about 0.02 MPa/s in this research，which can help get reliable data. The tested tensile strength of slate specimens，extracted in the ordovician-silurian formation of the Paleozoic period，in Changting，Fujian Province，is about 8.4 MPa. These research findings make preliminary bases for standardizing such kind of test method and test machine.