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We present the results of finite-element modeling of a YBCO thin-film superconductor deposited on a nonmagnetic substrate and on a weakly ferromagnetic substrate. The model was implemented using commercial software to calculate the ac loss in the presence of a sinusoidal external magnetic field applied perpendicular to the surface of the superconducting tape. A strategy is demonstrated to overcome the difficulties in the finite-element method due to the high aspect ratio of the YBCO film by using the computed values of ac loss for thicker samples to extrapolate the results to the actual physical thickness of the superconductor ( ~ 1 mum). The effect of the width of the weekly ferromagnetic substrate upon the ac loss of the superconductor film has also been studied.