We develop a mechanical model for catheters and other interventional devices which are steered by externally applied magnetic fields. Each device contains a permanent magnet near its distal tip. The external magnetostatic field, whose direction and magnitude can be selectively varied, is applied to the vicinity of the tissue where the medical procedure is being performed, in order to orient the catheter tip. At the same time, the length of the catheter is varied by a motorized advancer. The position and orientation of the catheter tip is determined in real-time by electromagnetic means. This information can be fed into a closed-loop control algorithm which would decide how to change the magnetic field and the catheter length. The model includes closed-form solutions of the equilibrium equations, which facilitates accurate estimation of the catheter configuration and the contact force. Once the device is at a target point, the control algorithm can modify the contact force applied to the tissue. Common applications include navigation inside the heart and coronary vessels, electrophysiology (atrial fibrillation, flutter and tachycardia, ventricular tachycardia, etc.) and interventional cardiology (angioplasty).