Abstract: This work proposes an finite element (FE) compression method to establish periodic representative volume elements (RVEs) of composites with high inclusion volume fractions efficiently and simply. The main procedures of the proposed FE compression method are given as follows: (1) Generation of the RVEs of composites with periodic and sparse inclusions using the random sequential absorption (RSA) algorithm, (2) FE compression of the generated periodic and sparse RVEs in step-1 to obtain the RVEs of composites with periodic and packed inclusions (in the FE mesh format) under the constrain of a periodic boundary condition, and (3) postprocessing to obtain the centroids (and orientation) of all the inclusions in the compressed RVEs with periodic and packed inclusions and generate the periodic RVEs of composites in the CAD format. Based on the proposed FE compression method, the periodic RVEs of spherical inclusions composites with the inclusion volume fraction up to 50.0% are generated. The distribution of the spherical inclusions in the generated periodic RVEs of composites is analyzed using the probability distribution function of nearest neighbor distance, the cumulative probability distribution function of nearest neighbor orientation angle, the Ripleys-K function and the pair correlation function, and the results show that the distribution of the inclusions in the generated periodic RVEs of composites is completely spatial and random. The elastic properties of different types of composites are homogenized using the FE homogenization method based on the generated periodic RVEs, and are then compared with those of the double-inclusion model and available experimental tests. It is observed that the elastic properties of the studied composites obtained using the FE homogenization method based on the generated periodic RVEs, the experimental tests and the double-inclusion model agree well, and it thus concludes that the proposed FE compression method is capable of generating the RVEs of composites with high inclusion volume fractions.