Due to overly-stiff effect, standard Finite Element Method (FEM) using triangular and tetrahedral elements gives upper bound solution of natural frequencies.  In order to improve the simulation results using low-order elements, one approach is to soften the overly-stiff of stiffness matrix to simulate the exact system, and the other is to match the mass matrix to the overly-stiff system. In this paper, the mass-redistributed method is further extended to analyse the eigenfrequency of solid systems. The mass-redistributed method is to modify the mass matrix of the discrete systems by shifting the integration points away from the Gaussian locations, while ensuring the mass conservation. Numerical examples including 2D and 3D problems have verified that Gaussian integration point in the mass matrix has a significant effect in the evaluation of eigenfrequency.