||The drilling of deep bore-holes in ice requires that the hole is filled by a liquid to compensate the ice-overburden pressure. Moreover, the hydrostatic pressure of the fluid should be exactly known in order to estimate the hole closure. The estimation of the hydrostatic pressure in the bore-hole can be made in two different ways. The first is the in situ measurements using pressure sensor, and the second is calculation of the pressure using the sampling of drilling fluid from different depths. The second method can be used also for prognosis of the hydrostatic pressure when the necessary density of the hole liquid is chosen. The paper includes the necessary equations for the calculation of hydrostatic pressure for one and two-compound liquids based on the pressure and temperature in the bore-hole. The measured and calculated densities are compared for the GISP2 bore-hole at Summit, Greenland, and it shows a high correlation. The difference between measured pressure and calculated pressure along most of the hole length doesn't exceed 0.12%.