It is shown that any given k-fold covering projection of graphs p: G1 → G2 can be embedded in a k-fold covering projection of closed orientable surfaces π: S1 → S2 in the sense that there are embeddings of G1 in S1 and G2 in S2 such that p is the restriction of π. In the case of a regular covering projection p, which is the quotient map with respect to some group action on G1, it is shown that there is a regular covering projection π of surfaces in which p can be embedded.
