In this paper, the antiplane harmonic dynamics stress of an infinite isotropic wedge with a circular cavity is analyzed for the first time by using a novel method with Green’s function, complex functions, and multipolar coordinates. A basic solution for the displacement field of an elastic half-space containing a circular cavity subjected to antiplane harmonic point force is employed as the Green’s function. Based on the Green’s function, the infinite wedge problem is equivalently transformed into the problem of a half-space divided by a semi-infinite traction free line. The equivalent problem is solved numerically to determine the dynamic stress field in the wedge at different apex angles and cavity locations. We show that the wedge angle, cavity location, and incident angle and frequency of the external load have significant effect on the dynamic stress of the cavity surface. The dynamic stress concentration factor on the cavity surface becomes singular when the cavity is close to the boundary of the wedge.