Rapid penetration of magnetic flux into a Meissner phase of the type-II superconductor is studied analytically and numerically. A sharp shock wave front of the magnetic induction is formed due to the non-analyticity of the resistivity at the transition from the mixed to the normal state. The shock wave magnetic induction and the temperature profiles move with constant velocity determined by the Joule heat produced by the electric current in the normal domain at the flux front. If the normal state resistance of the sample material is temperature dependent (like in HTSC), then the straight front shows instability. For a sufficiently small thermal diffusion constant a finger shaped avalanches are formed.