  A two-dimensional (2D) dislocation continuum theory is being introduced. The
present theory adds elastic rotation, dislocation density, and background
stress to the classical energy density of elasticity. This theory contains four
material moduli. Two characteristic length scales are defined in terms of the
four material moduli. Non-singular solutions of the stresses and elastic
distortions of an edge dislocation are calculated. It has been pointed out that
the elastic strain agrees well with experimental data found recently for an
edge dislocation in graphene.
