In this paper, we study a multicriteria shape design of a highly nonlinear mechanical 2D structure, namely the shape optimization of the aerosol can bottom. In fact, it is made depending on two criteria, the dome growth DG and the dome reversal pressure DRP, that define the resistance of the bottom against the internal pressure. This two criteria are known to be conflicting; therefore, a multicriteria optimization problem is formulated to represent the trade-offs among the design parameters. Due to the expensive time-consuming cost to solve this kind of optimization problems (e.g., capturing the Pareto front), the use of a surrogate model (e.g., metamodel) cheap to evaluate is mandatory. For this reason, we have developed an algorithm which is a coupling between the normalized normal constraint method (NNCM) and the radial basis function metamodel (RBF). The NNCM-RBF coupling was tested for several academic test cases and for our industrial problem and the obtained results clearly show the efficiency of our coupling to solve all the problems treated with a remarkable gain in the computational time.