The numerical solution of strain gradient-dependent continuum problems has been hindered by continuity demands on the basis functions. The presence of terms in constitutive models which involve gradients of the strain eld means that the $C0$ continuity of standard nite element shape functions is insu cient. In this work, a continuous/discontinuous Galerkin formulation is developed to solve a strain gradient-dependent damage problem in a rigorous manner. Potential discontinuities in the strain field across element boundaries are incorporated in the weak form of the governing equations. The performance of the formulation is tested in one dimension for various interpolations, which provides guidance for two-dimensional simulations.