The main distinctive features of ATLANTIDA3.1._2014, the first domestic program for the prediction of Earth tides, are discussed in comparison to similar programs of international authors, and some examples of the practical application of the program by different researchers are presented. The main functional features of the program are listed. Among them, the features for calculating amplitude delta factors of tidal waves for an oceanless Earth, as well as amplitude delta factors and phase shifts for an Earth with an ocean, tidal time series, and amplitudes and phases of the oceanic gravimetric effect, are especially distinguished. The theoretical developments included in the program are briefly described. The main differences of the latest version of the program are identified. The theoretical values of the amplitude delta factors for an inelastic self-gravitating rotating Earth, calculated with respect to the action of relative and Coriolis accelerations, as well as dissipation, are considered in detail. A total of 12 model variants are considered, which differ from each other by the inclusion or exclusion of separate factors affecting the result. The closeness of the results yielded by the program and the observations using the European superconducting gravimeters of the Global Geodynamic Project (GGP) is evaluated. It is shown that according to this criterion, our program surpasses the world’s most well-known counterparts. Tasks are listed that after their solution will expand the functional features of the program and clarify the results obtained so far.