A finite-difference method of calculating powerful underwater explosions using an artificial viscosity is described. An equation of state valid over a broad range of thermodynamic parameters is used for describing the properties of the water. Relatively weak explosions, where the compressibility of the water can be neglected or taken into account in the acoustic approximation, have been studied in [1–5]. This approach is not suitable for analyzing powerful underwater explosions, since it is necessary to have a complete thermodynamic description of the properties of the water over a broad range of pressures, temperatures, and densities. Several equations of state for water, valid over broad intervals of the thermodynamic parameters [6–9], have been proposed, although none has yet been generally accepted. Certain calculations have been made for very powerful underwater explosions using these complex equations of state (see, for example, [8]). In [10] a similar solution was obtained for the problem of a powerful point underwater explosion. The law of motion of the gas bubble was calculated in [11] and compared with the experimental data. The present study offers a numerical solution of the problem of an underwater explosion based on the equation of state obtained in [9]. The calculations involve a finite-difference method and the introduction of an artificial viscosity [12].