The paper addresses the problem of the development of robust algorithms for unwrapping the interferometric phase (IF) produced in the SAR interferometry. Two practicable methods are proposed based on the Green's first identify with properly chosen Green's functions satisfying the imposed Newmann's boundary conditions. These Green's functions are being found when solving the NEwmann's problem by means of the potential theory or through the representation of the Green's function as an infinite 2D series in the eigenfunctions of the Helmholtz equation. Then, the algorithms are being further elaborated using the method of regularization while searching for a gradient of the measured IF. Thus, the proposed approaches take into account the presence of the measurement noise in the IF. The developed algorithms proved to be stable both with respect to propagation of errors and with respect to local perturbations in the unwrapped phase due to inaccuracy of the measurement of a wrapped IF. The proposed algorithms allow their efficient numerical implementation using the fast Fourier transform. Experiments on data acquired by the satellite ERS-1 and supplied by CNES show high performance of both developed methods.© (1997) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.