A method is proposed for quantitative evaluation of the change in specific volume of refractory substance during a liquid-solid phase transition according to the surface shape of a flat ingot crystallized under conditions of central symmetrical heating. The accuracy of the estimate is up to 5–8%. With certain limitations the method is applied to a quantitative estimate of the volumetric effect of crystallization and in a number of cases melt density of the refractory materials themselves, for which obtaining information about melt density by any other method is impossible. Using the proposed method an estimate is provided for the density of molten yttrium and erbium oxides close to the melting temperature (for Y2O3 T m = 2440°C, for Er2O3 T m = 2430°C respectively).