Abstract: We have determined the crossing numbers of (Ｃｍ＋｛ｅ１｝)×Ｐｎ and (Ｃm+｛ｅ１｝＋｛ｅ２｝)×Ｐｎ(ｍ≥５，ｎ≥１)，ｅ１，ｅ２∈ｖｉｖｉ＋２（ｉ＝１，２，…，ｍ，ｉ＋２（ｍｏｄ　ｍ）).If the endpoints  are ｖｊ，ｖｊ＋２（ｊ＝１，２，…，ｍ，ｉ＋２（ｍｏｄ　ｍ）)，the endpoints of ｅ２ aren't ｖｊ＋１.

Key words: graph, drawing；crossing number；cartesian product；homeomorphism