We determine the band structure of graphene under strain using density functional calculations. The ab-initio band strucure is then used to extract the best fit to the tight-binding hopping parameters used in a recent microscopic model of strained graphene. It is found that the hopping parameters may increase or decrease upon increasing strain, depending on the orientation of the applied stress. The fitted values are compared with an available parametrization for the dependence of the orbital

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... erlap on the distance separating the two carbon atoms. It is also found that strain does not induce a gap in graphene, at least for deformations up to 10%.