The current research focuses on the design optimization of multi-cavity injection mold inserts taking into account the multidisciplinary nature of the injection molding system. The proposed modifications in the conventional multi-cavity-insert will allow flexibility in the production of a specified plastic part family. The use of the proposed flexible multi-cavity-insert can contribute to the reduction of overall mold material costs required for molding a part family. The flexible multi-cavity-inserts are designed to mold multiple part family members whose specifications vary within a permissible limit. Hence, there exists uncertainty in the input variables. Two approaches: robustness-based design optimization (RDO) and reliability-based design optimization (RBDO) are used to handle the uncertainty in the input variables. The optimal design for the proposed multi-cavity-insert considers the minimization of cycle time and pressure drop simultaneously. Therefore, a multi-objective optimization method is also used in the problem formulation. The present study solves the design problem using two approaches: the first approach uses RDO and the second approach uses RBDO within the multidisciplinary design optimization (MDO) framework. A numerical illustration of the design problem is presented specifying a part family with respect to a particular model of injection molding machine and a particular polymer material. Finally, Pareto optimal solutions are obtained that contain alternative combinations of cycle time and pressure drop. The specifications for manufacturing the flexible multi-cavity-insert are obtained from the optimal values of the design variables corresponding to the selected combination of cycle time and pressure drop. The proposed injection mold insert will be an economical solution for the production of small plastic parts having dimensional similarity.