Abstract: Linear elastic fuzzy finite element method is an effective technique used to analyze the uncertain response of structures due to the vague information in the elastic media.The time consuming problem of the solution of fuzzy governing equations is one of the main obstacles preventing fuzzy finite element method from development and application,even for elastic media.To seek reliable and feasible solving technique,emphasis is put on the study of the source of fuzzy characteristics of elastic media.It is proposed that fuzzy governing equations could be solved using operational principle of mono-source fuzzy number,when mechanical parameters are mono-source fuzzy numbers.Fuzzy stresses and fuzzy displacements could be obtained using synthesizing operation.Based on operational principle of mono-source fuzzy number,formulas of fuzzy stresses and fuzzy displacements of elastic media are deduced.Computed results of interval solution of fuzzy finite element method are compared with that of fast solution.The validity of fast solution is illustrated from the results.