The Large Hadron Collider (LHC) is designed to collide two proton beams with unprecedented particle energy of 7 TeV. Each beam comprises 2808 bunches and the separation between two neighboring bunches is 25 ns. The energy stored in each beam is 362 MJ, sufficient to melt 500 kg copper. Safety of operation is very important when working with such powerful beams. An accidental release of even a very small fraction of the beam energy can result in severe damage to the equipment. The machine protection system is essential to handle all types of possible accidental hazards; however, it is important to know about possible consequences of failures. One of the critical failure scenarios is when the entire beam is lost at a single point. In this paper we present detailed numerical simulations of the full impact of one LHC beam on a cylindrical solid carbon target. First, the energy deposition by the protons is calculated with the FLUKA code and this energy deposition is used in the BIG2 code to study the corresponding thermodynamic and the hydrodynamic response of the target that leads to a reduction in the density. The modified density distribution is used in FLUKA to calculate new energy loss distribution and the two codes are thus run iteratively. A suitable iteration step is considered to be the time interval during which the target density along the axis decreases by 15%-20%. Our simulations suggest that the full LHC proton beam penetrates up to 25 m in solid carbon whereas the range of the shower from a single proton in solid carbon is just about 3 m (hydrodynamic tunneling effect). It is planned to perform experiments at the experimental facility HiRadMat (High Radiation Materials) at CERN using the proton beam from the Super Proton Synchrotron (SPS), to compare experimental results with the theoretical predictions. Therefore simulations of the response of a solid copper cylindrical target hit by the SPS beam were performed. The particle energy in the SPS beam is 440 GeV while it has the same bunch structure as the LHC beam, except that it has only up to 288 bunches. Beam focal spot sizes of sigma = 0.1, 0.2, and 0.5 mm have been considered. The phenomenon of significant hydrodynamic tunneling due to the hydrodynamic effects is also expected for the experiments.