Deformations and thin-walled structures under the action of non-stationary loading with water or another fluid are studied. The constitutive equations include dependencies for the creep equation with a scalar damage parameter. An increase in load as a result of deformation is considered, and its growth over time due to an increase in irreversible creep deformations is taken into account. The stress-strain states in a thin plate are determined by an analytical method using an expansion in trigonometric series. The results show a significant change in the initial shape of the structure, as well as the acceleration of creep-damage processes over time. The presented models were used in calculations. Calculations determine sampling, which provides a stable solution to the edge problem and the convergence of numerous solutions over time. The plate is loaded with a liquid whose weight in an undeformed state is 10–30 times the weight of the structure. In this statement, we will consider the deformation of the plate during long-term operation for 100 days.