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Representations of braid group B n on n ≥ 2 strands by automorphisms of a free group of rank n go back to Artin. In 1991, Kauffman introduced a theory of virtual braids, virtual knots, and links. The virtual braid group V B n on n ≥ 2 strands is an extension of the classical braid group B n by the symmetric group S n . In this paper, we consider flat virtual braid groups F V B n on n ≥ 2 strands and construct a family of representations of F V B n by automorphisms of free groups of rank 2 n . It has been established that these representations do not preserve the forbidden relations between classical and virtual generators. We investigated some algebraic properties of the constructed representations. In particular, we established conditions of faithfulness in case n = 2 and proved that the kernel contains a free group of rank two for n ≥ 3 . [ABSTRACT FROM AUTHOR]