Motivation for the thesis is the vortex induced vibrations (VIV). To predict the fatigue life of an offshore cable subjected to VIV, the eigen frequencies of the system need to be known for the configuration of a cable subjected to a free span. The eigen frequencies are predicted with the use of both Euler-Bernoulli beam theory and cable theory by Irvine and Caughey. The commercial finite element (FE) software Abaqus is used to solve for the static sag and eigen frequencies with corresponding mode shapes modeled with beam elements in accordance with the Euler-Bernoulli beam theory. The governing assumptions is small strains, linear elastic and isotropic material. The stiffness effect due to change in arc length is included for bending contributions only. The influence of static sag on the dynamic response is discussed, and the conclusion is made that the static sag is an important effect. The soultions for cable theory is converging towards FE results for increasing span lengths, while solutions for beam theory is varying, depending on the type of boundary conditions present. The modal analysis is shown to include all geometric effects present in an oscillating offshore cable.