Chapter 4 introduced the concept of fracture mechanics for understanding earthquake rupture phenomena based on physical laws and presented elementary earthquake rupture models. However, a limitation of Chap. 4 is its focus on isolated semi-infinite cracks, largely due to elementary considerations. As a result, there is no discussion of crack size, making it impossible to explore how crack size affects rupture behavior. Additionally, Chap. 4 assumes the use of linear fracture mechanics, which leads to an inevitable infinite stress concentration at the crack tip. While this assumption may be acceptable in terms of energy rate balance, applying linear fracture mechanics to real earthquake ruptures poses problems, as typical crustal materials cannot tolerate such infinite stress levels. Moreover, it is unrealistic to assume that faults in the Earth's crust are isolated, especially in the vicinity of large-scale faults, where mechanical heterogeneity is well-documented, as mentioned in Chap. 1 . Although the analysis in the present chapter is limited to static conditions, it addresses not only singular finite-size cracks but also non-singular cracksSingular crack and the interactions between nearby cracks.