A vectorial interpolation problem is considered. In addition to the interpolation conditions taken at discrete points, a global, divergence-free condition is also prescribed. Utilizing the idea of the multi-elliptic interpolation, the divergencefree interpolation problem is converted to a generalized Stokes problem. To numerically solve this new problem, an Uzawa-type method and the method of fundamental solutions are proposed. In the second method, a linear system with large and dense matrix is to be solved, while in the first method, this problem is avoided. © 2011 Springer-Verlag Berlin Heidelberg.