The paper deals with mathematical modelling of nuclear fuel rod (FR) vibration in TVSA-T fuel assembly induced by pressure pulsations of coolant. The FR is modelled as a system consisting of two subsystems - fuel rod cladding and fuel pellets stack - that can possibly impact-interact. Besides, the cladding subsystem can possibly loose contact with spacer grid cells that is another source of strong mechanical nonlinearities. The contact forces in all the contact points are represented by the force-velocity-displacement characteristics that include both normal and friction forces. The influence of coolant cross-flow is analysed using partitioned approach to fluid-structure interaction description. The qualitative change of FRs motion and the change of fretting wear of the FR cladding are shown.