Summary: This paper presents a two-dimensional numerical procedure based on the boundary integral equations to model acoustic waves of finite-amplitude. The analysis is performed in the frequency domain. By applying the perturbation technique up to the second-order term, the governing differential equations are written as a system of two Helmholtz equations, one is homogeneous and the other one is inhomogeneous. Both are transformed into integral equations, which can be numerically solved without domain discretization by the use of the dual reciprocity boundary element method (DRBEM). To the authors' knowledge, this is the first application of DRBEM to nonlinear acoustics. The numerical procedure can be applied to predict the propagation of finite but of moderate amplitude acoustic waves in domains of any geometry. The final formulation is validated by comparison with an analytical solution derived by the authors.