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We study an effect of external radiation on the dynamics of Josephson junction shunted by an LC circuit. When the Josephson frequency is equal to the frequency of the circuit, additional stable resonant circuit branches appear in the IV -characteristic of the junction. The branches occur on the stable side of a narrow resonance peak, while the other peak side has a negative slope and is unstable. We show that the amplitude dependence of the Shapiro step width crucially changes when the Shapiro step is on the resonant circuit branch. These effects might give very important advantages for methods and technologies that exploit the response of Josephson junctions to microwave fields.