Abstract: The finite element method was used to model the moisture movement and strain in the wood supports of panel paintings, in response to changing climate conditions – temperature and relative humidity (RH). The material properties of lime wood (Tilia sp.), determined experimentally, were used in the modelling. Critical amplitudes of cyclic sinusoidal RH fluctuations generating strain of 0.002 in the most responsive tangential direction of the unrestrained, single wood panel, which the pictorial layer was assumed to endure without damage, were derived for the mid-RH region as a function of cycle duration, panel thickness and diffusion configuration. Panels do not respond significantly to diurnal fluctuations or shorter. The panels respond more and more significantly when the duration of the fluctuations increases until the panel fully responds to each cycle. These fluctuation periods are 14 and 90 days at 20 °C for a panel thickness of 10 and 40 mm, respectively, with two faces of a panel diffusively opened. Sinusoidal RH variations bringing about wood’s full response have the critical amplitude of ±6% RH, that is strain of 0.002 endangering the pictorial layer is produced at such amplitude in the tangential direction of the unrestrained panel.