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Application of stereo video in TV industry and consumer electronics becomes very popular recently. Thus, fast algorithm for stereo video coding is highly desired because of its huge inter-view computational redundancy. In our previous work we proposed an epipolar constraint based fast inter mode selection for stereo video using motion vector of blocks as a indicator of similarity, nevertheless, intra mode selection is also highly complex in standards like H.264/AVC. In this paper, a practical fast intra mode selection is proposed to eliminate the computational redundancy by exploiting inter-view dependency based on epipolar constraint. The proposed method does not rely on disparity estimation. Instead, a sliding window is employed to generate an intra mode candidate pool from macro-blocks on the epipolar line. The candidate pool is then rectified to remove invalid modes and improve accuracy. Finally, optimal prediction mode is selected from the candidate pool. The proposed method can significantly reduce the number of mode candidates/prediction directions compared to exhaustive mode selection by 79%. Experiments on 5 HD video coded in 1-frame demonstrate the overall coding time of one view is saved by 56% on average, with slightly video quality loss less than 0.1 dB.