A unified boundary integral equation is proposed to solve the sound radiation and scattering from the open/closed thin-bodies with arbitrary acoustic impedance in two- and three-dimensional domain. The proposed integral equation has the same influence matrix for both acoustic radiation and scattering problems and can synchronously solve the sound radiation and scattering from non-compact thin-body with arbitrary acoustic impedance condition, which can be applied to predict the noise of turbomachinery, pipe, and the muffler performance. In further work, the effects of moving surface and moving medium on sound radiation and scattering should be considered.