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Published in Petroleum Transactions, AIME, Vol. 210, 1957, pages 153–168. Paper presented at Petroleum Branch Fall Meeting in Los Angeles, Oct. 14–17, 1956. Abstract A theoretical examination of the fracturing or rocks by means of pressures applied in boreholes leads to the conclusion that, regardless of whether the fracturing fluid be of the penetrating or non-penetrating type, the fractures produced should be approximately perpendicular to the axis of least stress. The general state of stress underground is that in which the three principal stresses are unequal. For tectonically relaxed areas characterized by normal faulting, the least stress should be horizontal; the fractures produced should be vertical with the injection pressure less than that of the overburden. In areas of active tectonic compression, the least stress should be vertical and equal to the pressure of the overburden; the fractures should behorizontal with injection pressures equal to or greater than the pressure of the overburden. Horizontal fractures cannot be produced by hydraulic pressures less than the total pressure of the overburden. These conclusions are compatible with field experience in fracturing and with the results of laboratory experimentation. Introduction The hydraulic-fracturing technique of well stimulation is one of the major developments in petroleum engineering of the last decade. The technique was introduced to the Petroleum Industry in a paper by J. B. Clark, of the Stanolind Oil and Gas Co. in 1918, and since then its use has progressively expanded so that by the end of 1955 more than 100,000 individual treatments had been performed.