A possibility ofusing the vertical gravity gradient anomalies to the construction of the geodetic boundary value problem is presented m the paper. The kernel integral functions are given, m analogy to the Stokes' and Vening Meinesz 's functions. Presented approach may to be applied in geodetic practice taking into account recently needed precision of geoid and height differences by satellite and terrestrial data. Gradiometric information could be used for prediction of geoid undulation together with gravity anomalies. Results of the gravity gradient determinations on the territory of the geo- detic test fieid of the Warsaw University ofTechnology near Grybów (Cracow district) m sub-mountain area arę cited in the paper. The comparison between results of grawimetrie determinations and GPS levellingfor this region is given.