By using the finite element analysis (FEA) software in ANSYS Workbench, static and dynamic analysis were processed on the Straight Conjugate Internal Gear Pump.The stress concentration zone and location of large deformation that under the action of static load on the pump shell were found out. The natural frequencies and mode shape for the pump shell which impact the performance were obtained through the modal analysis. Thus the frequency and resonant amplitude at resonance occurred on the pump shell can be obtained under the cyclic loading, which provides a theoretical basis for the installation and use on the same types of gear pumps.