First, the coupling time constant and a coupling loss formula are derived for High T-c Super conductor (HTS) tapes, assuming their filamentary region to be an elliptical cylinder. Further, a hysteresis loss formula is given, treating the filamentary region as an elliptical cylinder and also considering the electric field-current density (E-j) characteristics to be represented with a power law. The formula of the hysteresis loss is applied in the magnetic field range much above of the full penetration field of the tape. These analytical results are compared with numerical results obtained by the finite element method. The formula of the hysteresis loss, derived for the multifilamentary composites, can be applied to the hysteresis loss in non-saturated individual filaments, assuming its shape as an ellipse. (C) 1999 Elsevier Science Ltd. All rights reserved.