A vibrating-element density meter is a mechanical oscillator with known properties, for example a tuning fork or a simple rod, driven to vibrate at a known frequency. The oscillator is immersed in a fluid and the resonant frequency measured. The density of the fluid can then be inferred. We consider an idealized meter immersed in two-phase flows of various types, and investigate whether a simple single-phase interpretation allows us to deduce the density of the mixture. We find that, when the density contrast between the two fluids is not great, the simple interpretation gives good results, for example in oil/water flows. However, when the density contrast is significant, for example in gas/liquid flows, the simple interpretation is highly inaccurate.