This research works is focused on the analysis of Fuzzy Finite-Element Method (FFEM) with the present of uncertainties. In considering a major engineering science problems, like damage processes or loading in consequence of real incident, uncertainty are present. Uncertainty is due to lack of data, an abundance of information, conflicting information and subjective beliefs. With that reason, the present of uncertainties is needed to avoid for prevent the failure of the material in engineering. The goals of this study are to analyzed and determine the application of FFEM by taking into consideration of the epistemic uncertainties involved toward the single edge crack plate and beam. Since it is crucial to develop an effective approach to model the epistemic uncertainties, the fuzzy system is proposed to deal with the selected problem. Fuzzy system theory is a non-probabilistic method, and this method is most appropriate to interpret the uncertainty compared to statistical approach when the deal with the lack of data. Fuzzy system theory contains a number of processes started from converting the crisp input to fuzzy input through fuzzification process and followed by the main process known as mapping process. In mapping process stage, the combination of fuzzy system and finite element method are proposed. In this study, the fuzzy inputs are numerically integrated based on extension principle method. Obtained solutions are depicted in terms of figures and tables to show the efficiency and reliability of the present analysis.