The plated structures are one of the most frequently used engineering structures. The object of this research work is the optimal design of curved folded plates. This work is an ongoing investigation. There are various solution methods to analyze this type of structures. Here the finite strip method is used. At first single load condition is considered, but later the multiple load conditions are used for the design. The base formulation is a minimum volume design with displacement constraint what is represented by the compliance. For the multiple loading two equivalent topology optimization algorithms are elaborated: minimization of the maximum strain energy with respect to a given volume or minimization of the volume of the structure subjected to displacement constraints. The numerical procedures are based on iterative formula which are formed by the use of the first order optimality condition of the Lagrangian-functions. The application is illustrated by numerical examples.