SIMD is one of the second round candidates of the SHA-3 competition hosted by NIST. In this paper, we present the first attack for the compression function of the reduced SIMD-256 and the full SIMD-512 (the tweaked version) using the modular difference method. For SIMD-256, we give a free-start near collision attack on the compression function reduced to 20 steps with complexity 2
. And for SIMD-512, we give a free-start near collision attack on the 24-step compression function with complexity 2
. Furthermore, we give a distinguisher attack for the full compression function of SIMD-512 with complexity 2
. Our attacks are also applicable for the final compression function of SIMD.