Electronic excitation-relaxation processes induced by ultra-short laser pulses are studied numerically for semiconductors and dielectric materials (Si, quartz). A detailed kinetic approach is used in the calculations accounting for electron-photon-phonon, electron-phonon and electron-electron scatterings. In addition, both laser field ionization ranging from multi-photon to tunneling one, and electron impact (avalanche) ionization processes are included in the model. Based on the performed calculations we study the relaxation time as a function of laser parameters. It is shown that this time depends on the density of the created free carriers, which in turn is a nonlinear function of laser intensity. In addition, a simple damage criterion is proposed based on the mean electron energy density rather than on critical free electron density. This criterion gives a reasonable agreement with the available experimental data practically without adjustable parameters. Furthermore, the performed modeling provides energy absorbed in the target, conditions for damage of dielectric materials, as well as conditions for surface plasmon excitation and for periodic surface structure formation on the surface of semiconductor materials.