Mathematical modelling of fast (microsecond) and superfast (nanosecond) regimes of electrical explosion of copper wires was carried out. The mechanism of electrical explosion was described as a process of propagation of the phase transition waves from outer boundary to the center of the wire. The expressions for estimation of a velocity of a phase transition waves were obtained. Typical phase tracks were obtained for micro- and nanosecond electrical explosion of copper wires. Metal-dielectric phase transition takes place without phase transition to two-phase state in skin at nanosecond explosion. The process of propagation of the evaporation waves is the mechanism of a wire electric explosion at microsecond regime.