A parallel radial basis function interpolation method for unstructured dynamic meshes. A radial basis function (RBF) interpolation method is implemented to be applied in computational fluid dynamics (CFDs) problems with dynamic meshes. The method has been tested with two challenging examples of dynamic meshing, the deformation of a pitching airfoil and a three-dimensional movement of a sphere, both discretized over viscous grids of around 5M control volumes. The work also includes a qualitative comparison of the RBF interpolation and the classical spring analogy formulations, which asserts that the new approach is far less costly and, besides, can achieve a good performance in preserving the mesh quality. In addition, the dynamic mesh adaptation has been coupled with a CFD solver, what has been validated on a benchmark problem consisting on a duct with a moving indentation. Finally, it is analyzed the parallel performance of the algorithm for the case of the deformable sphere, pointing out some key aspects that must be considered in order to improve the parallelization.