We present a model for the acceleration of energetic electrons by an ensemble of oblique shock waves at the hot spots of extended extragalactic radio sources. The energization of the electrons is based on the "shock drift" acceleration mechanism, using the adiabatic treatment, and electrons are subject to synchrotron losses as they travel between the shock fronts. We calculate numerically the energy distribution of electrons and the corresponding intensity of the radiation produced. We compare our results with the analytical solution of the Fokker - Planck equation. Our numerical and anaytical results agree well with the existing observations.
Key words : radio galaxies - radio hot spots - particle acceleration - synchrotron radiation - shock waves.