Analogy is a fundamental component of the way we think and process thought. Solving a word analogy problem, such as mason is to stone as carpenter is to wood, requires capabilities in recognizing the implicit relations between the two word pairs. In this paper, we describe the analogy problem from a computational linguistics point of view and explore its use to address relation extraction tasks. We extend a relational model that has been shown to be effective in solving word analogies and adapt it to the relation extraction problem. Our experiments show that this approach outperforms the state-of-the-art methods on a relation extraction dataset, opening up a new research direction in discovering implicit relations in text through analogical reasoning.