The method of calculating plates under the action of inertial loads during their movement with variable velocity is considered. The problem of the interaction of the airfield surface with the aircraft load is solved, at the moment of its movement, in braking mode, when landing on the surface in the form of an extended rectangular freely operable plate lying on an elastic base. When taking into account the nonlinear contacts of the chassis wheels with the plate, piecewise linear characteristics of contact stiffness are used. The vertical dynamics of the spatial model of the aircraft during the run is modeled by a system of rigid bodies with elastic-viscous bonds. To construct the methodology, the methods proposed earlier by the author of the article are used: a step-by-step method for solving problems of the relentless dynamics of structures and a method for calculating structures for the action of inertial and mobile force loads (the method of nodal accelerations).