An interesting behavior of thin-film magnetoimpedance elements in the relatively low megahertz (MHz) region is found experimentally when the width of the element is narrow and the thickness of elements is several micrometers. The impedance peaks and inductance shows a rapid drop at around 10 MHz when a bias field is applied to such elements. The impedance profiles of the elements were analyzed on the basis of a domain wall motion equation and bias susceptibility theory. Calculation of the domain wall motion equation when accounting for domain resonance explains the impedance behavior in the low MHz region. The rapid drop in inductance and peak in impedance can be attributed to the domain wall resonance. At a relatively higher frequency, above 100 MHz, the calculation of bias susceptibility while considering ferromagnetic resonance thoroughly explains the experimental behavior.