The intended steady-state operation conditions of the IFMIF-DONES target system are based on the D+ beam stationary running at full nominal power (5 MW). Nevertheless, critical situations can occur in case of unavoidable sudden events like beam trips. The instantaneous variation in the heating power deposited in the lithium when the beam is rapidly switched between-on and -off states leads to the thermal expansion, which is compensated by the compression of the target material, resulting in locally high pressures and a pressure wave propagating through the target towards the back wall. Besides tensile stress of the back wall structure caused by shock pressure waves, undesirable cavitation may occur, when pressure waves are reflected leading to negative pressures.For this purpose, analytical and numerical thermo-hydraulic analyses of the effects generated in the lithium during the beamon/beam-off switches are performed. The pressure wave development inside the Li-target has been analysed numerically with the CFD code Star-CCM+. The simulation of the thermal induced pressure in the Li-target shows that for normal operation conditions peak pressures of about 0,3 MPa can be reached. In both "beam-on" and "beam-off" cases a zone with a negative static pressure flow is forming in the Li-target. The results obtained from analytical and numerical analyses of the thermally induced pressure waves are discussed concerning potential cavitation and stability of the lithium free-surface flow. Simulation results served as input for the analysis of fatigue effects occurring in the target structure during sudden beamon/beam-off events.