The ingestion in aircraft engines is one of the actual problems related to the flight safety. One of possible reasons of ingestion in the gas-air flow duct of compressor is a formation of vortex core under an air intake on a runway surface during engine working on a stop. Calculations of the solid particles’ motion in wall-free concentrated vortexes, being the analogues of vortex core have been made in this paper. The numerical results have allowed to find peculiarities of behavior for particles with different inertia (different density and sizes) in vortexes of various intensity. Based on calculations and available experimental data a dimensionless criterion had been supposed, which determines the particles’ behavior in concentrated vortex structures. Estimations for maximal time of dynamic relaxation for particles involved in the air intake by vortex cores of different intensities have been made with use of this criterion. The knowledge of particles’ dynamics in the vortex cores formed near the air intake of aircraft engines is necessary to develop the methods to protect them from possible ingestion from the runway to ensure the flight safety.