In the analysis of the exterior sound field of a guitar, the vibration of the top plate is assumed as that of a clamped circular plate with its origin on the bridge, the side and back plates as rigid and sound hole as a neck of Helmholtz resonator. So that the known radiation impedance of the neck can be related with the sound pressure and the particle velocity on it. As a whole the problem can be solved by the Boundary Element Method (BEM). Consequently a reasonable result is obtainable for the sound field of a guitar though the computing time is taken long.