Introduction. The paper is devoted to research of the wave processes with free boundary based on the finite-difference method. Materials and methods. A mathematical model describing the dynamics of distribution of wave fluctuation was proposed on the basis of heterogeneous wave equation with the appropriate initial and boundary conditions. Discretization of the model was conducted using the integro-interpolation method taking into account the partial "filling" of computational cells. The

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... e modified alternating triangular iterative method of variational type with the highest rate of convergence in the class of two-layer iterative methods for solving the developed difference equations. Results. The developed discrete mathematical model for numerical simulation of wave propagation. The results of numerical experiments were obtained. The developed numerical algorithms and their computer implementation were used to research the dynamics of distribution of wave processes in the presence of the free boundary. Discussion and conclusions. The obtained results can be used for research of the dynamics of distribution of the wave processes with a free boundary and controlling in conducting experimental researches, evaluation and diagnosis, etc.