  Crack propagations in quasi-static fracture are studied theoretically. The
Griffith theory is applied to discuss a crack extension condition and motion of
crack tips in straight propagations. Stability of the straight propagations is
investigated based on the simple assumption that a curvature near the crack tip
is determined by a singular shear stress. It is shown that straight
propagations become unstable under ceatain conditions. Combined with boundary
effects, this instability leads to an oscillatory propagation of cracks. The
critical conditions are calculated quantitatively.
