Wave function expansion method and vibration theory are employed to study the out-of-plane response problem of the double degree of freedom vibration system installed on the half circular rigid platform on the half space boundary. The total displacement in the half space media was given using elastic wave theory,and the second order constant coefficient differential equations with which the double degree of freedom oscillatory system can also be given with the vibration theory,the unknown coefficients in the scattering functions can be obtained using the displacement and stress continuity conditions on the interface between the media and the rigid platform. And the variations of the relative displacement amplitude ratios of the rigid platform and the vibrators and the tangential stress concentration factor on the half circular interface can be given,the numerical results of given example show the correctness of the conclusions in the paper.