This paper is concerned with radiation and scattering of acoustic waves by obstacles of arbitrary shape embedded in a two dimensional medium. the Boundary Integral Equation method is used, which is known as the most useful one for external acoustic field problems in homogeneous medium. The non-uniqueness problem, which occurs at certain frequencies equal to the eigenfrequencies of the corresponding (but physically unrelated) interior problem, is overcome by Schenck method[4]. The discontinuity problem in body slope is studied with several different approaches. by comparing some numerical results with the known analytic solutions, the accuracy of solutions are confirmed. The method is applied to arbitrary shape bodies to study the scattering characteristics at near and far fields. Scattering due to triangular and rectangular bodies are calculated and compared with the results for the circular cylinder at different frequencies. Nearfield scattering fields around a NACA0012 airfoil are presented. The effects of the angle of incident wave are studied. The method is extended to multi-body problem. the calculation is carried out for two circular cylinder at several different distance between the cylinder. Finally, the two plates problem is studied which has the similar characteristic of an orang 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.