A stochastic model of ultra-short pulses interaction with a medium is based on simply the physical picture of matter and radiation, i.e., the matter as an ensemble of free electrons in the potential of ion lattice and radiation as a Poisson stream of laser light photons. In this model the basic reason of laser radiation absorption is collisional absorption of electrons. The iteration equation for photon stream intensity alteration after interaction with a single electron is obtained. Analysis of the suggested stochastic model permits us to find out criterion of pulse duration. According to this criterion ultra-short pulse is a pulse that does not change the medium's parameters (temperature, density, concentration of electrons, etc.) for a time of pulse duration. This definition is true for pulses, which have pulse duration less than the time of collision of electrons with ions, i.e. femtosecond and shorter pulses. It is shown that the main pulse parameter which determines the depth of laser penetration is pulse intensity. The pulse duration is a very important parameter, but its influence is not direct. The pulses of greater duration change media parameters for a time of pulse duration that leads to diminishing of the depth of laser penetration. For the laser light intensity is intratomic intensity or more in conductive media for laser frequency below plasma frequency the depth of laser penetration may arrive a few centimeters. For less intensity, the law of intensity attenuation is the well-known Bouguer-Lambert law. This proves possibility and adequacy of using the stochastic model of process of ultra short pulses interaction with a medium.