This work describes the dynamics of an underwater pipeline subjected to an incident flow composed of a uniform flow and a sinusoidal component. The motion equations of the pipeline and the fluid flow around the pipeline are solved simultaneously with a numerical model that considers in-line oscillations (one degree of freedom) and a second numerical model that additionally includes cross flow (two degrees of freedom). The amplitude response and drag forces on the pipe are compared for both models considering parameters such as the difference between the excitation and natural frequencies of pipelines and the relative value between the sinusoidal and uniform components of the incident flow. Important differences in numerical predictions of both models are observed when the excitation frequency is greater than the natural frequency of the system and when the amplitude of the oscillatory component of the incident flow is greater than the amplitude of the uniform flow.