Yamashita, T. and Ohnaka, M., 1992. Precursory surface deformation expected from a strike-slip fault model into which rheological properties of the lithosphere are incorporated. In: T. Mikumo, K. Aki, M. Ohnaka, L.J. Ruff and P.K.P. Spudich (Editors), Earthquake Source Physics and Earthquake Precursors. Tectonophysics, 211: 179–199. Earthquake prediction is one of the important problems with which seismologists are confronted. Much observational effort has been made to detect precursory surface deformation before earthquake occurrence. However, the physical mechanism to generate such precursory deformation is not fully understood. We, in this paper, theoretically study the growth process of strike-slip fault from nucleation to instability and a possibility to detect precursory surface deformation. Analyses are made on the basis of a breakdown zone crack model, which has been successfully applied in many aspects of earthquake rupture. We specifically attempt to simulate earthquake occurrence at the San Andreas fault, California, taking account of geological and geophysical conditions there. The most important parameters of the breakdown zone crack model will be the peak shear stress σ p near the crack tip, the sliding frictional stress σ f, and the critical slip displacement D c . For the depth variation of these parameters we assume a three-layer model, which is composed of a brittle upper layer, a plastic lower layer and an intervening semibrittle layer. We model the depth variations of σ p and σ f, modifying the shear resistance profile appropriate for the San Andreas fault obtained by Sibson. The depth distribution of D c is assumed to be constant D 0 in the brittle layer and to increase exponentially with depth in the semibrittle and plastic layers on the basis of the study of Ohnaka; the depth distribution of D c is described by two parameters, D 0 and S, the latter standing for the increase rate of D c in the lower two layers. Since there appears to exist much more uncertainty in the distribution of D c than in σ p and σ f, the effect of the parameters D 0 and S is specifically investigated. It is shown that the quasistatic crack tip growth turns unstable at a depth of 5 to 12 km. This will generally explain the seismological observation of focal depths of large earthquakes at the San Andreas fault. The depth of instability occurrence tends to deepen with increasing D 0. Our model predicts that the precursory stress change on the ground surface is larger and its duration is longer at a station closer to the surface trace of the fault. It is also shown that the precursory stress change is larger and its duration is longer when D 0 is in the range from 40 cm to 1 m. Precursory stress change will not be detected even at the instant of earthquake occurrence if D 0 is extremely small or extremely large compared with the values in this range. This finding suggests that precise knowledge on the value of critical slip displacement is required for the realization of reliable earthquake prediction.