A dedicated facility named High Radiation on Materials ͑HiRadMat͒ is being constructed at CERN to study the interaction of the 450 GeV protons generated by the Super Proton Synchrotron ͑SPS͒ with fixed solid targets of different materials. The main purpose of these future experiments is to study the generation and propagation of thermal shock waves in the target in order to assess the damage caused to the equipment, including collimators and absorbers, in case of an accident involving an uncontrolled release of the entire beam at a given point. Detailed numerical simulations of the beam-target interaction of several cases of interest have been carried out. In this paper we present simulations of the thermodynamic and the hydrodynamic response of a solid tungsten cylindrical target that is facially irradiated with the SPS beam with nominal parameters. These calculations have been carried out in two steps. First, the energy loss of the protons is calculated in the solid target using the FLUKA Nucl. Sci. Eng. 123, 169 ͑1996͔͒, which is based on a Godunov-type numerical scheme. The transverse intensity distribution in the beam focal spot is Gaussian. We consider three different sizes of the focal spot that are characterized by standard deviations, = 0.088, 0.28, and 0.88 mm, respectively. This study has shown that the target is severely damaged in all the three cases and the material in the beam-heated region is transformed into warm dense matter including a strongly coupled plasma state. This new experimental facility can therefore also be used for dedicated experiments to study high energy density matter.