Although theoretical studies on defects in continua have a long history, their main field of applications was limited to kinematical problems. Recent finding of rheological laws for generation of defects allows us to discuss dynamical problems, amongwhich is a problem of earthquake cycles - gradual accumulation of stress followed by its sudden release. This analysis is expected to pave the way for earthquake prediction.

In this review, we first sketch the models of earthquake cycles, using a simple friction law which controls the generation of defects on fault surfaces. We formulate a non-Markovian stochastic model by introducing viscoelasticity and fluctuation involved in the fault motion. Time asymptotic behaviors of the models so far obtained by simulation are summarized.

We then generalize the formulation. Deformation due to defects is described in a framework of differential geometry. Two notions, eigenstrain and eigenstrain production, are introduced to specify defects and rheology for generation of defects, respectively. With these notions, we derive an equation of motion of the system of defects. In this connection, we discuss Matsuno’s rheology where viscoelasticity is evoked by generation of defects.