Abstract: This paper considers the anti-plane dynamic response of a rigid semi-cytindri-cal foundation partially debonded from soil by using the wave function expansion method and singular integral equation technique.The debonding regions axe modeled as interface cracks. The mixed boundary conditions lead to a set of singular integral equations.Solving these equa-tions numerically,we obtain the displacement fields of the foundation and soil,and discuss the strength of the dynamic shear stresses on the bonding regions with the help of the dynamic stress intensity factors.