A sonar dome is basically designed and installed to protect sonar array from shocks, sea wave slaps and floating matters. The acoustic wave passing through sonar dome, however, can be distorted in magnitude and phase. This paper presents a numerical method for predicting the steady-state sound pressure on the surface of transducer array in the sonar dome and typical results of sonar beam pattern affected by sonar dome. A beam tracing model with phase information and a multi-layered elastic boundary model are involved. A full three-dimensional sonar dome is modeled as a GRP acoustic window, a rubber coated steel baffle and a rubber coated steel hull. A transducer array is modeled as thick steel cylinder. There are some assumptions such as incidence of plane wave, specular reflection on boundary and directionality of transducer element.