The structural member stiffness and strength of buildings are uncertain due to various factors resulting from randomness, material deterioration, temperature dependence, etc. The concept of sustainable building design under such uncertain structural-parameter environment may be one of the most challenging issues to be tackled recently. By predicting the response variability accurately, the elongation of service life of buildings may be possible. In this paper, it is shown that interval analysis in terms of uncertain structural parameters is an effective tool for evaluating the sustainability of buildings in earthquake-prone countries. All the combinations of uncertain structural parameters become huge numbers and this difficulty can be overcome by introducing the sensitivity or Taylor series expansion analysis. In order to demonstrate the usefulness and reliability of the proposed method, a shear building model is used including passive viscous dampers with supporting members. It is demonstrated that the proposed method is actually useful for the development of the concept of sustainable building design under such uncertain structural-parameter environment. (C) 2011 Elsevier B.V. All rights reserved.