This study examined vibrations in a conveying nonlinear string rested on a nonlinear elastic foundation. The Hamilton's principle was employed to derive the equations of motion for the string system. This nonlinear system was analyzed by using the method of multiple scales. The Fixed-point plots were used to study the frequency responses of the various modes and to verify the existence of internal resonance. The stability analysis of this system was studied by using Floquet theory. We applied the fourth-order Runge-Kutta method to obtain the Floquet transition matrix of the system. The Floquet multipliers (F.M.) was also used to determine the stability criteria of this system. The string system's stability range was vanished when the normalized string conveying speed went up to 0.12. Obviously, nonlinear characteristics play important role in the conveying string systems.