We describe a simple denotational semantics, using possible worlds, for a call-by-value language with ML-like storage facilities, allowing the storage of values of any type, and the generation of new storage cells. We first present a criticism of traditional Strachey semantics for such a language: that it requires us to specify what happens when we read non-existent cells. We then obtain our model by modifying the Strachey semantics to avoid this problem.