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Arc-transitive and edge-transitive graphs are widely used in computer networks. Therefore, it is very useful to introduce and study the properties of these graphs. A graphcan be called-edge-transitive (G-E-T) or-arc-transitive (G-A-T) ifacts transitively on its edges or arc set, whererespectively. A regular covering projection (C-P)is E-T or A-T if an E-R or A-T subgroup oflifts underIn this paper, we first study all-elementary abelian (E-A) regular covers of Wreath graphand then investigate (E-T) regular-covers of the Foster graph

Elementary abelian covers of the Wreath graph W (3, 2) and the Foster graph F 26 A