In this paper, the mathematk: al problem of the second fundamental problem of composite materials with a doubly periodic set of arbitrary shape cracks are investigated, and the interface are arbitrary smooth closed contours. At first, we establish mathematical models by using Muskhelisvili complex variable methods, change the primitive problems into searching complex stress functions whwh satisfy four boundary value problems and construct forms of the solution. then, under some general restrictions it is reduced to normal type singuiar integral equation, the unique olvability is proved mathematically.