A new effective method for computing the acoustic radiation and its sensitivity analysis of a structure subjected to stochastic excitation is presented. Previous work in the area of structural and acoustic sensitivity analysis systems was mostly focused on the deterministic excitation. New methods are developed to account for stochastic excitation. The structural-acoustic response is calculated using finite element method and boundary element method combined with stochastic analysis techniques. An accurate and highly efficient algorithm series for structural stationary random response analysis, pseudo-excitation method (PEM), is extended to acoustic random analysis in this paper, which was used to calculate structural random analysis in the past. So the acoustic radiation problems of random responses are transformed to the structural-acoustic harmonic analyses. This is a time-saving progress in comparison with traditional method. Based on the PEM, the acoustic radiation sensitivities of the structure are developed in emphasis that are transformed to harmonic sensitivity analyses. They are validated by comparing with the results of finite difference sensitivity method. Numerical examples are given to demonstrate the effectiveness of the methods and the program.