We have developed 2D Arbitrary Lagrangian Eulerian (ALE) code in the cylindrical r-z geometry. The ALE method overcomes problems with Lagrangian moving mesh distortion by mesh smoothing and conservative quantities remapping from Lagrangian mesh to smoothed one. The flyer target experiments [1,2] performed at the Prague PALS laser facility are simulated by the developed code. The thin flyer disc is irradiated by intense laser beam and ablatively accelerated up to very high velocities (till 150 km/s) against a solid target. The high velocity impact of disc flyer on the target creates a crater. The high velocity impact simulations cannot be accomplished by standard Lagrangian code without the ALE method. The simulation results for several laser energies in 120-390 J range and laser basic and third harmonics compare reasonably with experimental data which include disc flyer impact velocities and crates sizes.