Numerical simulations on retrieving the 3-D structure of the sound-speed inhomogeneities based on data on the horizontal refraction angle (HRA) of acoustic modes have been performed. The inversion proceeds in two stages. At the first stage the values of propagation constants of different acoustic modes at the nodes of a horizontal grid are calculated. The corresponding procedure represents a linear 2-D problem which is solved for different modes independently. At the second stage the coefficients of the expansion of the variation of the sound-speed profile with respect to some set of empirical orthogonal functions are calculated based on already determined values of propagation constants. This stage represents a 1-D nonlinear problem which is solved for different nodes of the horizontal grid independently. When error-free HRA data were used in the numerical simulations, the 3-D sound-speed field was retrieved perfectly. Then the HRA data were artificially distorted with random errors. It was found that the relative error of the retrieved values of the propagation constant of modes is proportional to the error in HRA (expressed in radians). Corresponding relative error in retrieved values of sound speed is in its turn proportional to the relative error in propagation constants. When the level of HRA error has been chosen according to the level arising from distortions caused by internal waves, the rms error in the retrieved sound-speed values for the situation considered appeared to be about 0.7 m/s.