Abstract An explicit finite difference code, ELWA, has been developed for solving a three-dimensional (3D) formulation of the damped elastic wave equation for a soil medium in the time domain. The code was implemented on a 8K processors massively data-parallel computer. In this paper, a description is given of the mathematical model forming the basis for the code as well as of its application towards explaining the occurrence of extreme ground and structural vibrations during a rock concert in Gothenburg, Sweden. During two rock concerts held at a large outdoor stadium in Gothenburg, in the summer of 1985, the part of the audience standing on the pitch in front of the stage started to jump in time to the music. This rhythmic jumping caused the soil deposit below to vibrate heavily, leading to severe vibration in the flexible superstructure of the stadium. The vibrations became so severe in the upper parts of the stands that the audience left their places. Residents in the neighbourhood of the stadium complained of heavy vibrations in their respective residences. A model of the soil medium under the stadium arena is described along with the excitation forces used to model audience behaviour when listening to rhythmic and excitable music. Using ELWA, an analysis of soil vibrations for these conditions shows that the reflection of vibrations from the solid rock underlying the clay deposit upon, which the stadium is based, causes standing waves to arise at the associated resonant frequencies. These waves will be transmitted to the stadium superstructure through soil–foundation interaction. The most important parameters controlling the wave amplitude were found to be the thickness of the clay deposit and the frequency of loading.