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Here we report the results of an experimental study where we measure the hydrodynamic force acting on a plate which is lifted from a water surface, suddenly starting to move upwards with an acceleration much larger than gravity. Our work focuses on the early stage of the plate motion, when the hydrodynamic suction forces due to the liquid inertia are the most relevant ones. Besides the force, we measure as well the acceleration at the centre of the plate and the time evolution of the wetted area. The results of this study show that, at very early stages, the hydrodynamic force can be estimated by a simple extension of the linear exit theory by Korobkin (J. Fluid Mech., vol. 737, 2013, pp. 368-386), which incorporates an added mass to the body dynamics. However, at longer times, the measured acceleration decays even though the applied external force continues to increase. Moreover, high-speed recordings of the disc displacement and the radius of the wetted area reveal that the latter does not change before the disc acceleration reaches its maximum value. We show in this paper that these phenomena are caused by the elastic deflection of the disc during the initial transient stage of water exit. We present a linearised model of water exit that accounts for the elastic behaviour of the lifted body. The results obtained with this new model agree fairly well with the experimental results.