Special cross-section shape matrices may present better performance than the circular matrices in high gradient magnetic separation (HGMS). The particle capture of elliptic matrices in the transversal HGMS was investigated previously but no experiments were conducted. In the present paper, experiments with circular and elliptic matrices are conducted in the transversal HGMS, providing that the short axis of the elliptic matrices is equal to the diameter of the circular matrices. Results show that the elliptic matrices have higher hematite recovery than the circular matrices. However, the experimental results are inconsistent with previous theoretical analyses. It is therefore necessary to reconsider and improve the particle capture models of circular and elliptic matrices in the transversal HGMS. The magnetization state of the matrices has great influence on the particle capture in HGMS. Previous investigations are all based on the assumption that the matrices are saturated by the magnetic induction. In this article, the magnetic field around the unsaturated matrices is derived and the generic particle motion equations of particles around the circular and elliptic matrices in transversal HGMS are deduced. Analyses with the improved particle capture models show that the ratio of the particle capture radius of the elliptic matrix to that of the circular matrix decreases with the increase of magnetic induction. The elliptic matrices have higher particle capture efficiency at q/b = 1 (ratio of matrix spacing to matrix short axis) than the circular matrices in relatively low magnetic induction, which agrees well with the experimental results. Based on the theories constructed in this paper, systematic investigations of elliptic matrix in transversal HGMS will be conducted in follow-up studies, including its separation performance for actual weakly magnetic minerals.