This paper is concerned with radiation and scattering of acoustic waves by obstacles of arbitrary shape embedded in a two dimensional medium. The Boundary Element Method is used. which is known as the most useful one for external acoustic field problems in homogeneous medium. The nonuniqueness problem. which occurs at certain frequencies equal to the eigen-frequencies of the corresponding interior problem. is overcome by Schenck method. By comparing some numerical results with the known analytic solutions. the accuracy of solutions is confirmed. The method is applied to arbitrary shape bodies to study the scattering characteristics at near and far fields. The method is extended to multi-body problem. The calculation is carried out for two circular cylinders at several different distance between the cylinders. Finally. the two plates problem is studied. which has the similar characteristic of an organ pipe. It turns out that the mode pattern inside the plates depends on the incident wave frequencies and the high amplitude pressures are obtained inside the plates at the resonent frequencies.