This study examines the energy deposition of runaway electrons (REs) on tungsten targets, considering the effects of electron beam incidence angles, magnetic field strengths, and target thicknesses. Two energy distributions are analyzed: a monoenergetic beam and a Maxwellian distribution. Simulations are performed using the GEANT4 Monte Carlo code to accurately model particle–matter interactions, including secondary emissions and energy loss mechanisms. For perpendicular incidence, energy deposition in the tungsten target increases with electron energy until reaching a peak, then declines at higher energies. The peak shifts toward higher energies as the target thickness increases. In contrast, for tangential incidence representative of realistic tokamak wall loading the fraction of deposited energy is highest at lower electron energies (0.1–1 MeV), whereas the absolute deposited energy continues to increase with electron energy. Magnetic fields significantly influence tangential interactions by enhancing the return of reflected electrons to the target, leading to greater energy deposition, especially at lower energies. In contrast, for perpendicular incidence the magnetic field strength has only a minor effect on deposition. Additional analyses show that, in tangential incidence, a considerable fraction of the reflected energy is redistributed onto adjacent tungsten tiles due to magnetically guided electron motion. Moreover, the contributions of transmitted and reflected photons and neutrons were quantified to determine their share in the overall escaping energy. These results underline the importance of jointly considering the electron energy spectrum, incidence geometry, magnetic field strength, and tungsten thickness in the design of plasma-facing components, in order to more accurately assess heat loads and mitigate potential damage from REs in tokamak environments.