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There have been many progresses in the stereo matching problem. However, some remaining problems still make stereo matching difficult. Occlusion is one of such problems. In this paper, we propose a new stereo matching model that addresses this problem by using an effective visibility constraint. By considering two images simultaneously, complex geometric configurations regarding the visibility of a pixel becomes simplified, so that the visibility constraint can be modeled as a pairwise MRF. Also since the proposed model enforces the consistency between two disparity maps, the final results become consistent with each other. Belief propagation is employed for the solution of the modeled pairwise MRF. Experimental results on the standard data set demonstrate the effectiveness of our approach. [ABSTRACT FROM AUTHOR]