Impossible differential cryptanalysis and zero-correlation linear cryptanalysis are two of the most useful cryptanalysis methods in the field of symmetric ciphers. Taking the non-linear components into consideration, this article proposes a method for searching the impossible differentials and zero-correlation linear approximations of SIMON based on a technique of SAT. In applications, the proposed method is used to find more impossible differentials and zero-correlation linear approximations for 11-round SIMON. Furthermore, this tool can be used to prove whether there are impossible differentials (zero-correlation linear approximations) in certain rounds of SIMON, particularly for certain subset of input and output patterns of differences (masks). Utilizing this tool, the security of SIMON as well as the choice of its parameter set when resisting the impossible differential cryptanalysis are also explored.