In this paper, the bending of curved uniaxial elements with non-constant stiffness is discussed, which have large displacements due to their high slenderness. The basic differential equation to determine large displacements is implemented for elements made from materials that follow Hook's rheological model. The effect of large displacements was taken into account in the determination of bending moments by considering the equilibrium state on a deformed system. The components of the displacement vector are determined generally in the form of power series, or for the special case of loading in the finite form. Another two numerical examples are calculated. The first example is solved using a calculator and represents an element of constant curvature whose width of the rectangular section varies linearly. It is loaded with compressive force, clamped at the lower point, and the upper point is free. The second case is solved analytically in the finite form and represents an element of non-constant axis curvature and rectangular cross-section width. It is loaded with Mo moment at both sites. The lower seat is rotatably clamped, while the upper one can move freely along the joint of the two seats.