The electromagnetic interaction of colliding beams causes beams to be perturbed as they approach each other. As luminosity depends on colliding beam parameters, luminosity is influenced and its calibration via the van-der-Meer scan is biased. Currently, this effect is estimated using Gaussian models for particle densities in colliding beams. However, for more precise calculations, models of beam-beam force that account for the beam shape deviations from Gaussianity should be found. In this article, the model for beam-beam nteractions of Q-Gaussian colliding beams is presented. It is believed that this model adequately describes non-Gaussian tail shapes. For LHC conditions, a comparison with the regular Gaussian model is performed. The evolution of the effect during the van-der-Meer scan is demonstrated.