Current Fused Deposition Modeling (FDM) technologies deposit material as flat layers. The result is a “stair-case” effect on non-vertical or horizontal surfaces, and compromised part strength because of weakness between the laminations. This paper describes a FDM method through which layers of build material are deposited as curved layers following the shape of the part, thus removing the stair-case effect and creating parts that have an even strength distribution over their entire surface. Support material is first deposited as conventional flat layers, and build material is then deposited over the support structure following the curves of the part. The paper discusses a proof of concept of the system, the algorithms used to generate the curve paths for the deposition head, and examines the challenges and possibilities of this technology, including the capability of including composite materials.