Abstract: An external periodic load is applied on a pinned-pinned pipe conveying fluid, and the nonlinear forced vibration for this system is explored by the multidimensional Lindstedt-Poincaré (MDLP) method. According to the analysis, when the second natural frequency of the system is nearly thrice the first one, and the excitation frequency is near the natural frequencies, a principal resonance with intense internal resonance may occur. The characteristics of responses for the first two modes are investigated in detail. Numerical examples reveal the rich and complex dynamic behaviors caused by an internal resonance. The influence of excitation amplitude on the internal resonance is analyzed and it is shown that some internal resonances of the system will decline and even disappear as the excitation amplitude increases. The convenience and efficiency of the MDLP method in researching nonlinear dynamics are also demonstrated.