The behaviour of a tungsten first wall is studied under the irradiation conditions predicted for the different operational scenarios of the European laser fusion project HiPER, which is based on direct drive targets and an evacuated dry wall chamber. The scenarios correspond to different stages in the development of a nuclear fusion reactor, from proof of principle (bunch mode facility) to economic feasibility (pre-commercial power plant). This work constitutes a quantitative study to evaluate first wall performance under realistic irradiation conditions in the different scenarios. We calculated the radiation fluxes assuming the geometrical configurations reported so far for HiPER. Then, we calculated the irradiation-induced evolution of first wall temperature and the thermomechanical response of the material. The results indicate that the first wall will plastically deform up to a few microns underneath the surface. Continuous operation in a power plant leads to fatigue failure with crack generation and growth. Finally, crack propagation and the minimum tungsten thickness required to fulfil the first wall protection role is studied. The response of tungsten as a first wall material as well as its main limitations will be discussed for the HiPER scenarios.