A theoretical modeling framework is proposed to follow shape and residual stress evolutions of layered flexible display structures with respect to deposition, ambient temperature and relative humidity conditions. This model couples the mechanical equilibrium equations of elastic layers with transient heat and mass transfer equations for the predictions of temperature and moisture content inside the structure. Experimental data have been used to calibrate this model. For that purpose, nanometric silicon nitride barrier layers on polyimide substrates were investigated. The thermo-hygro-mechanical behavior of individual materials, including the water diffusion and sorption properties of polyimide were measured. Simulation results were then compared with experimental measurements of the curvature dynamics of samples subjected to isothermal relative humidity jumps. It is concluded that accurate simulations require accounting for the dependence of the water concentration-dependent diffusion coefficient.