It is important for an architect or a construction manager to easily and accurately estimate the heating and cooling demand of a residential building with a different envelope design in the early design phase. To achieve this objective, this study aimed to develop a nine-node-based Lagrangian finite element model for estimating the heating and cooling demand of a residential building with a different envelope design, which can be useful for an architect or a construction manager in the early design phase. This study was conducted in the following steps: (i) definition of the building envelope design elements; (ii) establishment of a standard database through energy simulation; and (iii) development of a Lagrangian finite element model. The prediction performance of the proposed nine-node-based model was improved in comparison with the four-node-based model. It was concluded that the prediction performance of the proposed nine-node-based model was superior to that of the four-node-based model. For the heating demand, RMSE(9-node, heating) (61.2), MAE((9-node, heating)) (45.1), and MAPE((9-node, heating)) (1.18%) of the proposed nine-node-based model was lower than that of the four-node-based model (73.9, 53.2, and 1.36%). For the cooling demand, RMSE(9-node, cooling) (71.5), MAE((9-node, cooling)) (55.3), and MAPE((9-node, cooling)) (8.24%) of the proposed nine-node-based model was lower than that of the four-node-based model (84.1, 61.1, and 8.71%). The series of processes used in this study could be applied to any other energy-saving technique or to a new/renewable energy system. It could also be extended to any other country or sector in the global environment. (C) 2014 Elsevier Ltd. All rights reserved.