The influence of an insulating crack on the dielectric breakdown of polymers and ceramics is evaluated by finite element modeling. Measured dielectric breakdown and relative permittivity for epoxy resin and alumina specimens were used as inputs for the numerical model. An insulating crack was modelled in the center of the material, with its longitudinal direction aligned parallel and perpendicular to the electric field direction. The intensity of the electric field increases up to 17 times, confined within the crack when the crack was perpendicular to the field. The presence of a crack parallel to the field does not cause large disturbances on the electrical field distribution. The measured dielectric breakdown for both materials were similar to those obtained by the model with the crack in perpendicular direction.