Abstract: In this work the process of earthquake rupture is studied by means of the theory of fracture mechanics. It is believed that the phenomenon of earthquake is essentially caused by the rupture of rock media under low shear gtress conditions. It is the result of continual development of cracks from the stable to the final unstable state. The change of stress and displacement in the process of crack development has been analysed from which one can see that the stress at any point where rupture will occur always undergo a rise from its initial value (0) to the yielding strength (y) before rupture. After rupture, the stress on the crack surface will drop to a low value near zero. The displacements before and after rupture can be calculated by the formulae of theory of elastic ity but at the instance of rupture, the inelastic displacement at the tips of crack is not given by the same formulae, which may be approximately obtained from the slide displacement formula in fracture mechanics. According to the dislocation model, it is because that the dislocation D(, t) from which elastic wave radiation field has been calculated is jusjt the inelastic displacement, at the instant of rupture. Therefore, to estimate stress drop and calculate earthquake dislocation by elastic displacement formulae will be erroneous. If the earthquake dislocation is estimated by the slide displacement formula in fracture mechanics, more adequate formulae for calculating the total energy ET(ET=yDS, y= yield strength, D= average dislocation, S = area of the fault surface) released by an earthquake andthe initial stress 0(0=Dmax/L4y/(1-) 1/2L=length of fault ) can be deduced.Using these formulae, the total energy ET released by some earthquakes and the initial stress To are estimated and listed in the table 1 and 2. They are more reasonable than before. They demonstrate that (1) most earthquakes take place under low initial stress, about 100-200 bars, (2) the total energy released by an earthquake is about one order of magnitude higher than the seismic wave energy.