The European Spallation Source, ESS, will be based on a 2.5-GeV, 50-mA superconducting proton linac deli- vering 5 MW of beam power to a rotating tungsten target. ESS is a challenging project in many respects, not the least with respect to RF power and RF sources. Because of the high power, relative beam losses must be very small to avoid activation and allow hands-on maintenance of accelerator components. The beam-dynamics calcula- tions required to ensure these low beam losses are thus another challenge. This paper gives an introduction to ESS and the ESS linac, discusses briefly computational aspects in general, and presents specific examples of computational problems from beam dynamics and RF cavity design as well as efforts initiated to benchmark beam-dynamics codes for beam parameters relevant to ESS.