The deformation and fracture of graphene under uniaxial tension is simulated in the framework of quantum mechanics. The deformation forces are calculated as energy gradients from a microscopic strain coordinate in the quantum mechanics approximation. The strain and fracture characteristics (Young's moduli, stiffness coefficients, critical forces and fracture stress) are calculated using macroscopic relations of the linear theory of elasticity. The emphasis in the work is on the analysis of the effect of model sizes, defects and surface modification on the strain characteristics of graphene. The simulation results are compared with available experimental data. © 2010.