A method for severing or weakening materials. Explosive cords are placed in grooves on the upper surface of the material to be severed or weakened. The explosive cords are initiated simultaneously to introduce explosive shock waves into the material. These shock waves progress toward the centerline between the explosive cords and the lower surface of the material. Intersecting and reflected waves produce a rarefaction zone on the centerline to fail the material in tension. A groove may also be cut in the lower surface of the material to aid in severing or weakening the material.