LetRbea commutative ring with identity. AnR-module (ideal ofR)Ais called amultiplication module (ideal)if for each submoduleNofAthere exists an idealIofRwithN=I A. We give several characterizations of multiplication modules. Using the method of idealization we show how to reduce questions concerning multiplication modules to multiplication ideals. For example, we show that ifSis a commutative R-algebra and ψ:M→anR-module homomorphism whereMis a multiplicationR-module andNis anS-module, thenSψ(M) is a multiplicationS-module.