The Milky Way's satellite galaxies and globular clusters (GCs) are known to exhibit an anisotropic spatial distribution. We examine in detail this anisotropy by the means of the inertia tensor. We estimate the statistical significance of the results by repeating this analysis for random catalogues that use the radial distribution of the real sample. Our method reproduces the well-known planar structure in the distribution of the satellite galaxies. We show that for GCs several anisotropic structures are observed. The GCs at small distances, 2<R<10kpc, show a structure coplanar with the Galactic plane. At smaller and larger distances, the whole sample of GCs shows quite weak anisotropy. Nevertheless, at largest distances the orientation of the structure is close to that of the satellite galaxies, i.e. perpendicular to the Galactic plane. We estimate the probability of random realization for this structure of 1.7 per cent. The bulge-disc GCs show a clear disc-like structure lying within the Galactic disc. The old halo GCs show two structures: a well-pronounced polar elongated structure at R<3kpc that is perpendicular to the Galactic plane, and a less pronounced disc-like structure coplanar with the Galactic disc at 6<R<20kpc. The young halo GCs do not show significant anisotropy.