Crack shape, orientation, size and growth due to hydraulic fracturing will be investigated as a problem in three dimensional elasticity theory. Since the opening of the crack by hydraulic fracture, the pressurizing of the treatment fluid, the teaking off of the fluid, and the thermal cracking are simultaneous events, the theory of e lasticit y will be coupled with fluid mechanics and the theory of heat conduction. The results, which include the coupling of elasticity and fluid inclusion, will be obtained by analytical techniques so that they can be presented with analytical formulae when possible.

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