Density index (or relative density) is the measure of compaction of non-cohesive soils naturally compacted as a result of geological processes. It also is used for compaction control of non-cohesive soils built in hydraulic embankments. Hydraulic engineering embankments and hydro-melioration systems should be characterized by high load capacity, tightness, and durability, and low water-permeability and low deformability. These features are obtained as a result of compaction of earth layers. Direct examinations of all parameters required for calculation of density index of each earth layer (dry density of soil in embankment and minimum and maximum dry density of soil) is time consuming. Dependencies between the dry densities (minimum and maximum) and graining of non-cohesive soils were developed in order to simplify the test procedure of density index. Statistical linear regression and artificial neural networks were applied.