Analysis of low frequency axial drilling dynamics from block velocity input to surface weight on bit (SWOB) or differential pressure outputs, shows significant regional variation. This range in dynamics poses a robustness challenge for automated drilling control systems. Many factors influence drilling dynamics such as pipe stiffness, mud properties, tortuosity, friction, bit design, and BHA geometry. A simple analytic model representing axial drilling dynamics is described and compared to a finite element drilling model and to drilling data. The analytic model shows that axial drilling dynamics may be represented by a first-order transfer function with a time constant dependent on axial stiffness and drillabillity.