This talk focuses on developing radial basis function (RBF) collocation methods for both the frequency-domain and time-domain obstacle wave scattering scattering problems. For the frequency-domain elastic wave scattering problems, the unbounded domain problem is truncated using a transparent boundary truncation method with Dirichlet-to-Neumann (DtN) map and PML technique. Then global or local collocation methods based on RBFs are applied; For time-domain acoustic scattering problems, non-reflecting boundary conditions are constructed on the truncated boundary by first deriving a DtN map in the frequency domain and then applying an inverse Laplace transform. The numerical schemes combining the Newmark time integration with RBF collocation methods are proposed. Numerical simulations for irregular obstacles demonstrate the effectiveness of the proposed methods for both kinds obstacle waves scattering problems.