Due to the existence of randomness and fuzziness in engineering problems, the reliable performance prediction is very complex. In addition, in the early design stage of a new product, the insufficient information on uncertainty further aggravates the difficulty of performance prediction and robustness evaluation. This paper suggests a new reliability analysis method using possibility theory to evaluate constraint feasibility even with insufficient uncertainty data in design variables. In order to save the computing time, two strategies of approximating performance constraints are proposed: 1) design sensitivity-based method and 2) dynamic Kriging-based method. Through applications to analytic example and engineering problem, the proposed methods are investigated and discussed.Index Terms-Finite-element analysis (FEA), fuzzy measures, possibility theory, reliability analysis, uncertainty in design variable.