© 2015. Dynamic penetrometers have been used for offshore oil and gas industry applications such as pipeline feasibility studies and anchoring systems, and military applications including naval mine countermeasures and terminal ballistic studies. The main challenge of using dynamic penetrometers is the interpretation of their test results in order to deduce the mechanical properties of the penetrated soil via empirical or theoretical relations. Recently, a robust numerical method based on the Arbitrary Lagrangian-Eulerian (ALE) technique has been developed for analysing dynamic penetration problems and used to investigate a smooth penetrometer free falling into a uniform layer of clayey soil. Numerical as well as experimental results indicate that the penetration characteristics, including the impact energy, total time, and total depth of penetration, depend on the mechanical properties of the soil including its stiffness and strength parameters as well as the geometry of the penetrometer and its initial impact energy. In this study, the ALE method is employed to study the effect of shear strength increasing with depth (a common condition of seabed deposits) on the penetration characteristics of a free falling penetrometer. Conducting more than two thousand numerical simulations has shown that there is an approximate quadratic relation between the final embedment depth of a FFP penetrating into a non-uniform clay soil and the combined kinetic energy on contact with the soil and subsequent loss in potential energy of the penetrometer.