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Indoor climate fluctuations are regarded as one of the major risks for the emergence of damage in historical works of art. For a safe preservation of their art objects museums try to minimize this risk, which is typically done by imposing strict limitations on the indoor temperature and humidity conditions. The high energy demand resulting from this approach, however, undermines the aim of preeminent museums to execute a sustainable preservation strategy of their collections. A rational improvement of this aspect asks for detailed information on the history of museum objects, complemented by a thorough comprehension of the failure and deformation behaviour of museum objects under indoor climate fluctuations. Accordingly, in this paper the hygro-mechanical response of mock-ups of historical Dutch cabinet door panels made of oak wood is examined under several relative humidity variations. In specific, the mock-ups were subjected to (i) an instantaneous decrease of 40% relative humidity, (ii) eight successive, instantaneous drops of 5% relative humidity, and (iii) a varying relative humidity profile ranging between 35 and 71%. The shrinkage characteristics of mock-ups are translated to their damage susceptibility using an analytical hygro-mechanical bi-layer model. This model shows that restrained hygral shrinkage may originate from: (i) a difference in moisture content across the thickness direction of the panel, or (ii) a directional difference in the coefficient of hygroscopic expansions of structural components forming a coherent connection. The first type of shrinkage occurs in the outer regions of the panel thickness, while the second type of shrinkage takes place at the cleated ends. Further, by accounting for the age-dependency of the fracture strength of oak wood, a clear distinction can be made between the damage susceptibility of new door panels and historical door panels present in museum cabinets. The six main conclusions of the experimental study—conveniently summarized at the end of this paper—provide a scientific basis for the understanding of shrinkage cracks and dimensional changes observed on decorated oak wooden panels in historical Dutch cabinets, and thus may assist in advising museums on future sustainable preservation strategies and rational guidelines for indoor climate specifications.