Considering the increasing importance of stereo image compression and Fractal geometry becoming one of the most important fields of modern science ,we applied fractal image compression based on quadtree portioning method and global search algorithm , on a group of stereo image pairs . As the stereo image consists of two planar images , left and right .Both the left image ( reference image ) and the disparity map between left and right images , were compressed using fractal compression . We applied both block matching algorithm and Semi Global Method (SGM)to obtain the disparity map. The left image and the depth map were reconstructed using fractal decompression while the right image (target image ) was reconstructed using the reconstructed left image , disparity map and the error image between the original right image and the reconstructed right image that was build from the left image and the disparity map . The results were evaluated using quality objective measures which are MSE (Mean Square Error ) and PSNR (Peak Signal to Noise Ratio) and efficiency objective measures which are CR(Compression Ratio) and compression time . The results were compared with JPEG compression of stereo pairs based on Discrete Cosine Transform DCT and JPEG2000 compression of stereo pairs on stereo image based on Discrete Wavelet Transform DWT .