It is the aim of this work to develop and extend the theory of undamageable materials to graphene. An undamageable material is a material where the value of the damage variable remains zero throughout the deformation process. It is anticipated that the constitutive equations for undamageable graphene can be modeled with differential equations for the case of graphene. The equations are solved for three cases: n = 1, n = 2, and the general case of n. It is hoped that undamageable graphene can be achieved in the laboratory in the near future when the manufacturing technology advances so as to produce such materials.