Abstract : We give two different formulas to evaluate the conditional Laplace transform of a regime switching Cox Ingersoll Ross model. One using the property of semi-affine of this model and the other one using analytic approximation. Then we study the pricing of bonds issued by two firms considering the default and the correlation risk. In fact, we consider two firms with correlated default times and we obtain numerical formula for the bonds prices considering the regime switching market credit notations and the correlation between the two firms. Finally we give some numerical illustrations.