A finite element analysis was performed on panel painting structures subjected to changes in relative humidity. Measured Young's modulus values and humidity expansion coefficients were used to define the properties of materials characteristic to northern and southern European panels. Models of northern panels simulated white oak with two layers of oil paint, while models of southern panels simulated cottonwood with gesso and two oil paint layers. In both cases, the properties of the oil paints were input for lead white and Naples yellow respectively. Influence of radial/tangential grain orientation, panel thickness, and structural support were investigated through various humidity changes. Results are presented in the form of stress in the wood, gesso, and paint layers as well as curvature of the painted surfaces. Methods of reducing panel curvature with structural support are discussed, which involve applying a frictionless cradle, wood battens, or verso gesso layer. Verification of the model was performed with a derivation of general stress equations for a cradled painting with no friction between the slider-bars and the panel. A comparison of derived and parametric results confirms accurate behavior of the model.