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For the first time in this paper, by using semi-analytical scaled boundary finite element method (SBFM), a perfect nano garphene sheet or defected ones were simulated and their mechanical behavior had been investigated. In this analysis, the atomic carbon bonds were modeled by simple bar elements with circular cross- sections and then the scaled boundary finite element relations were formulated based on the geometry of the model. The obtained results from SBFM were compared to those obtained from molecular dynamic method which showed that the SBFM can be used as a continuum mechanics model with high accuracy in mechanical analysis of both perfect and defected nano graphene sheets. Existence of structural defects in nano grapheme sheets decrease the strength as well as fracture strain in a considerable manner. It can be noted that in a defected nano grapheme sheet, the fracture stress decreases more than 34% while fracture strain decreases more than 50%. In the cases that instead of using bar elements, whole area is considered as a continuum sheet and in order to obtain a similar geometry to those problems have bar elements, no material zone be modeled by zero elastic properties, the results show considerable errors.