Magma movements are almost universally associated with volcanic deformation. The Mogi (1958) and McTigue (1987) models link observed surface displacements to behaviour within inaccessible magmatic plumbing systems. Mogi and McTigue models are well-used due to their computational simplicity and ease of application, but both models are limited by their assumptions about the deformation source and its embedding domain. Domain assumptions, including elasticity, homogeneity, and flat topography, have been previously described and corrected for. Whilst recognising the limits of these models, their frequent use in the literature requires an objective assessment of their utility against more sophisticated Finite Element (FE) models, their operational limits (radius-to-depth ratio, ε) and their relative merits in the light of limited field data. Here, we relax the source assumption of a small ε. We simulate volcanic deformation using Mogi, McTigue and FE models - the latter unrestricted by ε - to validate the maximum ε for which the analytical models can be applied, and to compare analytical and FE interpretations of deformation data from Kīlauea Volcano, Hawai'i. We find that analytical and FE models correspond for deformation sources with a range of ε that is wider than previously suggested limits. The differences between simulated surface displacements (forward modelling) and estimated deformation source parameters (inverse modelling) are less than 5% when ε < 0.37 (Mogi) or ε < 0.59 (McTigue). Misfits between analytical and FE models depend on whether radial or vertical displacements are considered simultaneously or independently, and on the values of source radius and depth - not only their ratio, as was assumed previously. There is little or no difference between best-fitting source parameters inferred using Mogi, McTigue and FE models at Kīlauea Volcano, despite the high ε of the system geometry, but sometimes poor correspondences between model results and GNSS observations. Our results demonstrate that Mogi and McTigue models can be applied to volcanoes with a wider range of magma reservoir radii and depths than was hitherto supposed, but previously-established corrections for domain simplifications are necessary to accurately interpret volcanic deformation.