We present a computational study of Edney type shock-shock interactions between an oblique shock and a bow shock in front of a circular cylinder. Both cold and hot hypersonic test cases were considered and the results revealed the main features characterizing the type III and type IV of interaction, without and with the jet impinging on the cylinder. The simulations also predicted qualitatively the complex flow structure observed in the experiments and the pressure and heat peak on the surface of the cylinder.