Based on the potential theory and the finite element method, the added mass of objects moving in fluid was studied. Firstly, the added mass of a ball in the infinite domain and the added mass of a cylinder in lateral motion in a tube were calculated to verify the validation of the codes. Then the added mass for slender cylinders with different end shapes moving axially in a long tube fluid was analyzed. The results show that under a given diameter of the tube, the added mass for the slender cylinder is proportional to its length. And the slope of the linear relationship increases rapidly with the decrease of the distance between the slender cylinder and tube wall. Moreover, when the length of the cylinder is much larger than its diameter, the shapes of the cylinder ends have little influence on the added mass.