We analyze thermal, mechanical, and electromagnetic effects produced by the laser irradiation of opaque materials under different densities of power and different atmospheric pressure and present a condition of plasma formation in dependence on the power density. The regression models presented determine the qualitative relationships between the power density of laser pulse irradiation on the irradiated surface and the maximal value of magnetic induction of pulse magnetic field in deep vacuum. On the base of these models we can also determine the relationships between the atmospheric pressure and the maximal value of induction of pulse magnetic field generated by the laser plasma.