In this work, a multi-objective mixed integer linear programming (moMILP) model is presented for the design and planning of sustainable closed loop supply chains. It includes strategic decisions such as facility location, definition of transportation modes, technology selection and allocation, as well as tactical decisions. The model includes four objectives: 1) The economic pillar, measured through the net present value (NPV); 2) the environmental pillar, which includes Life Cycle Assessment (LCA), through the application of the ReCiPe methodology; 3 and 4) The social pillar measured using two socio-economic indicators applied by the European Union in its Sustainable Development Strategy. The applicability of the model is demonstrated through a representative supply chain case study. Results show that the different objectives influence the supply chain structure and translate in significantly different and conflicting decisions, showing the importance of such type of models to better understand the decisions implications on the different dimensions of sustainability.