<p>Buckling failure in submarine cables presents a prevalent challenge in ocean engineering. This work aims to explore the buckling behavior of umbilical cables with damaged sheaths subjected to compression and bending cyclic loads. A finite element model is devised, incorporating a singular armor wire, a rigid core, and a damaged sheath. To scrutinize the buckling progression and corresponding deformation, axial compression and bending cyclic loads are introduced. The observations reveal that a reduction in axial compression results in a larger number of cycles before buckling ensues and progressively shifts the buckling position toward the extrados and fixed end. Decreasing the bending radius precipitates a reduction in the buckling cycle number and minimizes the deformation in the armor wire. Furthermore, an empirical model is presented to predict the occurrence of birdcage buckling, providing a means to anticipate buckling events and to estimate the requisite number of cycles leading to buckling.</p>