Current practices for assessing the thickness of growing ice include drilling and coring. This is inherently risky and motivates the use of a stand-off method. Laser Doppler vibrometry is a potential technique, however, the interpretation of vibrometer signals must be informed by a physical understanding of ice subjected to mechanical vibrations. The vibrational response of growing, thin ice is largely unknown. For thick ice, adequate predictions for the vibrational response assumes ice behaves as an elastic plate. It is hypothesized that thin ice responds in a fashion somewhere between an elastic membrane and an elastic plate. A modal test of thin ice growing within an insulated plastic basin was conducted over the course of two tests. The resulting dataset spans a range of ice thicknesses from 8 to 45 mm. Examination of Bode and Nyquist plots showed that the two lowest observable ice resonances, as measured at the center of the ice sheet, exhibit a dependence on ice thickness distinctly different from a fixed elastic plate loaded by a half-space of water. Preliminary finite-element analysis calculations indicates that the basin wall compliance is a significant factor in modifying the ice resonance versus thickness relationship.