The exact solution of inextensible catenaries in Cartesian coordinates is utilized to propose an efficient two-node cable element for static analysis of three-dimensional cable structures. This element can consider out of plane inclination without using any transformation matrices. Since the element is formulated within the framework of large curvature assumption, cables with large sag, as encountered in long-span cable-stayed bridges and suspension bridges, can be modeled accurately. The proposed element also accounts for the thermal effects. By defining the stiffness component as the ratio of infinitesimal load increment to infinitesimal increase in length, explicit entries of the tangent stiffness matrix are derived through equating the total differentiation of the strained length and the elastic elongation of the cable. The tangent stiffness matrix is available in a closed form and the need of taking the inverse of the flexibility matrix, which is faced in the solution procedure of elastic catenary, is eliminated. The robustness of the suggested technique is established through investigation of significant case studies, including slack and pre-tensioned spatial cable networks. Excellent agreement between the present results and those found in the literature indicates the versatility of the proposed scheme.