The effect of dispersion on the propagation of linear rectangular pulses of magnetostatic waves in YIG films is studied. With surface magnetostatic waves propagating in YIG films and composite ferrite-insulator-metal structures, it is demonstrated that, for the near-rectangular phase-unmodulated input pulse and the distance between input and output transducers equal roughly to half the dispersion length of the pulse, the FWHM of the output pulses is 50–60% of the initial value. This fact can be used for estimating the dispersion coefficient of magnetostatic waves.