In this paper a model-based approach is taken to identify certain geometric and/or material parameters for a structure. Specifically, the focus is on determining the average thickness of a thin, fully-clamped plate undergoing free vibration. The methodology is described and then implemented in an experimental setting using the measured free response of a plate. The practical SHM scenario driving this investigation is corrosion, since the extent of corrosion damage is often described in terms of the effective thickness of the plate, i.e. how much of the plate's thickness is still structurally intact. Data are gathered from three resistive strain gages, placed at arbitrary locations and orientations. Using the experimental response and a finite element model, a Bayesian approach is taken to estimate the plate thickness, h. This thickness could then be used to infer the extent of the damage, had corrosion been present. The results show that even with limited, noisy vibration data valuable information regarding the geometry and material characteristics of a plate can be successfully estimated.