Given a regular and normal element ω in an associative ring A, we study model structures on the category F(A; ω) of module factorizations. Explicitly, we define the homotopycategory of module factorizations and realize it as the homotopy category of a certain exact model structure. Furthermore, we construct three abelian model structures on F(A; ω) via the one on the category of left A-modules, and show that the zeroth cokernel and kernel functors induce Qullien equivalences. Some applications of these results in Gorenstein homological algebra are also described. This talk is based on a joint work with Liping Li, Li Liang and RongminZhu.