A semi-analytical method of solving the problem of dynamic stress concentration of arbitrary underground structure under the effect of blast waves was introduced.Using the Fourier transform theory, the shock waves (in the forms of SH-waves) can be converted into frequency bands. After employing complex functions and conformal mapping, the admittance functions of various underground structures were obtained. Then,the problem of the time domain dynamic stress response of underground structure can be easily solved through the Fourier inverse transform. At last, the results and curves of the dynamic stress for the square, triangle and horseshoe cavity were presented.