Аннотация:The paper presents a solution of the contact problem for a periodic two-level system of axisymmetric punches and a viscoelastic half-space. The case of a constant nominal pressure applied to the punch system is considered. The variation of the real contact area in time and the conditions that provide the contact of the punches of both levels with the half-space, are investigated. The influence of the geometric parameters of the punch system and the mechanical properties of the viscoelastic half-space on the contact characteristics is analyzed. Numerical results are presented for the system of punches located in the nodes of a square lattice and penetrated into a viscoelastic half-space modelled by a standard linear solid. It is shown that the real contact area may increase greatly if the second level punches come into contact with the half-space at some instant of time.