Many design problems in engineering are typically multiobjective, under complex nonlinear constraints. The algorithms needed to solve multiobjective problems can be significantly different from the methods for single objective optimization. Computing effort and the number of function evaluations may often increase significantly for multiobjective problems. Metaheuristic algorithms start to show their advantages in dealing with multiobjective optimization. In this paper, we formulate a new cuckoo search for multiobjective optimization. We validate it against a set of multiobjective test functions, and then apply it to solve structural design problems such as beam design and disc brake design. In addition, we also analyze the main characteristics of the algorithm and their implications.