We shall study the following problem: given n > 2 subsets A1, A2, . . . , An of an arbitrary finite field Fq with q elements. One should define when there exists a finite natural number N such that N-fold sumset of the set A1 · A2 · . . . · An covers all the field Fq. This problem is not solved in general, but some special cases the problem is studied. The purpose of this talk is to present these partial results and discuss possible difficulties that may occur in study of the problem.