regime of photon energy up to 24-25 keV with the pulse duration of a few tens of femtoseconds, possibly reduced further down to a few femtoseconds. The advent of such light sources stimulated rapid advances in many scientific disciplines ranging from atomic physics [6,7], study of molecules and chemical reactions [8,9], to clusters [10,11] and macroscopic objects [12-14] exposed to intense laser fields. They are actively used for creating and probing plasmas [15,16], hot dense matter [16][17][18] and warm dense matter [19,20]. Lower fluences of FELs are used to investigate structural changes within solid-state matter [12,[21][22][23][24]. These new light sources have also found a broad interest in the fields of nanophysics [25], molecular physics and biophysics [26].Insulators irradiated with femtosecond X-ray FEL radiation are observed to undergo a sequence of processes [12,27]. During the pulse, the photoabsorption excites electrons from the valence band, or deep atomic shells, to unoccupied conduction band states. The deep shell atomic holes then decay via Auger processes, which are the dominant relaxation channel for light elements (low-Z) [28]. An Auger decay promotes one more electron from the valence to the conduction band, following the relaxation of the deeper shell hole into the upper shells or the valence band. In case of heavy elements, with multiple shells, an intraatomic Auger cascade involving many steps over different shells is possible, ultimately ending up with multiple holes in the valence band. This process occurs typically on the few femtosecond timescale. The released photo-and Auger electrons scatter inelastically (so-called impact ionization of valence band or deep shell electrons of the material), or elastically (scattering on atoms or phonons without ionization of the target). Each impact ionization event excites one more electron into the conduction band. The impact ionization cascading typically occurs on the femtosecond Abstract Modern X-ray free-electron lasers (FELs) provide pulses with photon energies from a few tens of eV up to the tens of keV and durations as short as only a few femtoseconds. Experimental pump-probe scheme with a FEL pump and a visible light probe of a solid-state target can be used for the pulse-duration monitor on a shot-to-shot basis.To study the electron cascading in different materials used for pulse-duration monitor, XCASCADE, a Monte Carlo model of the X-ray-induced electron cascading within an irradiated target is developed. It is shown here that the electron cascade duration is sensitive to a choice of material. An appropriately selected target can significantly shorten the electron relaxation times. The grounds, upon which such a choice of the material can be made, are discussed. The results suggest that for photon energies of 24 keV, one could achieve direct monitoring of the pulse duration of 40 fs. Further deconvolution of the electron density into the contribution from the pulse itself and from the secondary cascading can increase the resolution up ...