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This paper discusses the applying of 2-D MUSIC spectral estimation algorithm used in ISAR imaging. The motivation for applying 2-D MUSIC algorithm is to improve resolution and remove side-lobe effects compared to the conventional imaging techniques based on Fourier transform. This paper makes two principal contributions to the 2-D MUSIC algorithm. First, it proved that 2-D MUSIC algorithm using spatial smoothing technique is equivalent to 1-D MUSIC algorithm. Second, the effectiveness and uniqueness conditions for 2-D MUSIC algorithm are derived and demonstrated. Simulations illustrate that only when the effectiveness and uniqueness conditions are met can the unique imagery of target using 2-D MUSIC algorithm be obtained; otherwise there will be Â¿artifactsÂ¿.