By using the complex variable function theory and the conformal mapping method, the scattering of plane shear wave (SH-wave) around an arbitrary shaped nano-cavity is studied. Surface effects at the nanoscale are explained based on the surface elasticity theory. According to the generalized Yong–Laplace equations, the boundary conditions are given, and the infinite algebraic equations for solving the unknown coefficients of the scattered wave solutions are established. The numerical solutions of the stress field can be obtained by using the orthogonality of trigonometric functions. Lastly, the numerical results of dynamic stress concentration factor around a circular hole, an elliptic hole and a square hole as the special cases are discussed. The numerical results show that the surface effect and wave number have a significant effect on the dynamic stress concentration, and prove that our results from theoretical derivation are correct.