Peculiarities of propagation of short optical pulses through resonantly absorbing fractal media are investigated in the work using methods of numerical simulation. The fractal object was modeled by a one-dimensional structure with its parameters being similar to generalized Cantor dust. The dependence of transmission of such a medium on its Hausdorff dimension in some cases was shown to have a nonmonotonous character. Interpretation of the results obtained is also given.