Airborne magnetic tensor gradiometers using SQUID technology are currently being trialed, posing the problem of how to best recover information from this new type of data. This paper investigates the possible advantages of magnetic field tensor data for interpretation of an area of shallow volcanics in southern Victoria, Australia. Source models for TMI anomalies over volcanic pipe or fissure sources have been used to generate synthetic magnetic field tensor data. Inversion of the TMI and tensor data indicates that tensor data can substantially improve resolution in mapping these shallow volcanics. Inversion of the TMI data cannot differentiate between dipping bodies with induced magnetization, and vertical bodies with remanent magnetization. The simulated magnetic tensor data accentuates differences between these models and confirms that magnetic tensor data would provide greater sensitivity in resolving the magnetization direction, and thereby the dip of the sources.