Radial basis function-generated finite difference (RBF–FD) methods have recently been proposed as very interesting for global scale geophysical simulations, and have been shown to outperform established pseudo-spectral and discontinuous Galerkin methods for shallow water test problems. In order to be competitive for very large scale simulations, the RBF–FD methods needs to be efficiently implemented for modern multicore based computer architectures. This is a challenging assignment, because the main computational operations are unstructured sparse matrix–vector multiplications, which in general scale poorly on multicore computers due to bandwidth limitations. However, with the task parallel implementation described here we achieve 60–100% of theoretical speedup within a shared memory node, and 80–100% of linear speedup across nodes. We present results for global shallow water benchmark problems with a 30 km resolution.