There is reason to believe (I.V.Volovich's hypothesis) that on Planck scales the geometry of space-time is non-Archimedean. However, the mechanism of geometry substitution during the transition to Planck scales has not been studied. The report will address this problem in the language of metric geometry. In particular, an explicit construction will be proposed for the geodesic between Archimedean and non-Archimedean spaces in the Gromov-Hausdorff space.