Building on the beam equation, this paper derives a realistic and versatile 3D model of tether/cable/umbilical dynamics and approximates it via the Finite Element Method (FEM). This FEM implementation/approximation can be executed in real time, when the model accuracy is not of prime concern for the application at hand, or in an offline fashion, when the model accuracy is essential. Our model allows for different time-varying forces (e.g., wind gusts, sea currents, waves, etc.) acting along the cable. However, unlike the related works, where tether bending and stretching are mutually independent resulting in unrealistic tether elongations, our implementation takes into account the tether length, which in turn imposes coupling among transversal and longitudinal tether displacements. Our work is motivated by applications of tethered robots such as Unmanned Underwater Vehicles (UUVs), most commonly Remotely Operated Vehicles (ROVs) and Unmanned Aerial Vehicles (UAVs). In such applications, the tether is typically kept under tension leading to “small” tether displacements and the absence of deformations and entanglements, which is why the beam equation is selected to start with. However, partially owing to the attention paid to the tether length, our dynamic model behaves well even for “larger” displacements as illustrated in Gazebo ROS using a tethered ROV whereas the tether itself is implemented in Matlab via FEM.