This work examines the surface/interface effect on the dynamic stress around a cylindrical nanoinclusion embedded in an elastic semi-infinite slab subjected to antiplane shear waves, and the nanosize effect is considered. The wave function expansion method is employed to express the wave fields in the nanosized structure. The traction free boundary conditions at the three edges of this structure are considered and satisfied by using the image method. The analytical and numerical solutions of the dynamic stress concentration factor around the nanoinclusion are presented. Analyses show that the three edges of the nanosized structure manifest different effects of the dynamic stress around the nanoinclusion. The size effect is also related to the interface properties, the wave frequency of incident waves, and the material properties ratio of the nanoinclusion to matrix. To show the accuracy of the results for certain given parameters, comparison with the existing results is also given.