The object of study in this article is a thread subjected to a nodal load, as an element of suspended structures, such as suspension bridges. The relevance of the research lies in the necessity to enhance accuracy in selecting the geometric parameters of the thread. The methods employed in the research include the finite element method in its classical mixed form and the method of generalized unknowns. As a result of the calculations performed on internal forces in sections of the thread and the thrust, dependencies of internal forces on geometric and physical parameters have been obtained, and the most effective relationships between the geometric parameters of the thread have been identified. In particular, based on the provided graphs, it can be noted that the allowance for the thread—elongation relative to the span between supports is most appropriately chosen within the range of 10% to 20% of the span length, as a reduction in allowance leads to a sharp increase in forces within the thread and thrust. Conversely, increasing the allowance beyond 20% results in a decrease in forces and thrust that cannot compensate for the increase in load due to self-weight, nor justify an increase in the height of supporting structures. Previously, in engineering practice, the relationship between geometric parameters (the length of the thread and the sag) was often accepted empirically; however, this study provides precise explanations for these relationships, and the results obtained may be beneficial for practical design applications.