In the specific case of curved cable-stayed bridges, the horizontal component of the load introduced by the stay cables on the deck is variable, concentric and dependent on the connection configuration between the tower and the cables, becoming a challenge in the design of these type of bridges. Hitherto, designers have dealt with this challenge in different ways, either by optimizing the position of the tower and its geometric characteristics, or by modifying the morphology of the stay cable system. This paper proposes the use of funicular and anti-funicular curves of the horizontal concentric load, introduced by the stay cables, to design the curved deck directrix, reducing lateral forces on the deck under the self-weight hypothesis. For the design of the deck directrix, two different formulations are considered: one discrete by means of summations and the other continuous by means of non-linear differential equations. Both formulations study the two possible signs of the axial force which will govern the design (funicular and anti-funicular curves). A least squares approximation is developed to facilitate the implementation of these formulations. The paper introduces a method to liberate the deck from its most important lateral loads, i.e., the concentric loads introduced by the stay cables. This way, it develops a deck dominated by axial forces instead of lateral ones (Bending moment with vertical axis, Mz, and lateral shear force, Vy), which can be critical for its design and decrease the stay-cable system efficiency. It explains, by different methods, how this directrices vary with different design decisions, so that the designer can develop the directrix that suits his design. Finally, two examples of directrices are given as a conclusion.