Let G = (V, E) be a simple loopless finite undirected graph. We say that G is (2-factor) expandable if for any non-edge uv, G + uv has a 2-factor F that contains uv. We are interested in the following: Given a positive integer n = |V |, what is the minimum cardinality of E such that there exists G = (V, E) which is 2-factor expandable? This minimum number is denoted by Exp 2 (n). We give an explicit formula for Exp 2 (n) and provide 2-factor expandable graphs of minimum size Exp 2 (n).