Eco-Industrial Parks (EIPs) and Industrial Symbioses (IS) provide cost-effective and environmental friendly solutions for industries. They bring benefits from industrial plants to industrial parks and neighborhood areas. The exchange of materials, water and energy is the goal of IS to reduce wastes, by-products and energy consumption among a cluster of industries. However, although the IS design looks for the best set of flow exchanges among industries at a network level, the lack of access to accurate data challenges the optimal design of a new EIP. IS solutions face uncertainties. Considering the huge cost and long establishment time of IS, the existing studies cannot provide a robust model to investigate effects of uncertainty on the optimal symbioses design. This paper introduces a framework to investigate uncertainties in the EIP design. A multi-objective model is proposed to decide the optimal network of symbiotic exchanges among firms. The model minimizes costs of multiple product exchanges and environmental impacts of flow exchanges. Moreover, this paper integrates the analysis of uncertainties effects on synergies into the modeling process. The presented models are depicted through optimizing energy synergies of an industrial zone in France. The efficiency of single and multiple objective models is analyzed for effects of the identified uncertainties. In addition, the presented deterministic and robust models are compared to investigate how the uncertainties affect the performance and configuration of an optimal network. It is believed that the models could improve an EIP's resilience under uncertainties.