Original binary image can be reconstructed without any distortion by MS(morphological skeleton) image. Though we reduce some points in a MS image, there is no problem to reconstruct original image by it. And then, there are two methods of LMS and GMS which reduce the redundant points of a MS image. The redundancy degree of a GMS image is zero and it is less than that of LMS. And then, GMS image is the best thing of the three kinds of morphological skeleton image to enhance the compression efficienty by the Elias code. But there are continous SKF=1 points in a GMS image whenever using 2 dimensional structureing element. Those points in a GMS image gives rise to a bad compression efficiency. And then, solving this problem, this paper proposes hybrid structuring elements algorithms for binary image compression.