Experiments of circular and elliptic cylindrical matrices with the same cross-section area in the axial high gradient magnetic separation (HGMS) had been conducted previously. The results showed that the elliptic matrices present much better performance than the circular matrices at lower magnetic induction (< 0.35 T). However, previous theoretical analyses indicated that the capture efficiency of the circular and elliptic matrices were almost the same. A very important factor was not considered in the theoretical analyses, namely the applied magnetic induction Almost all the theoretical studies concerning the basic principles of HGMS in the past were based on the premise that the matrices were saturated by the magnetic field. In the present paper, particle capture behaviors of the circular and elliptic matrices in the axial HGMS were studied with varying the magnetic field. The generic particle motion equations were derived and the particle capture cross sections of the matrices were compared, for both the case that the matrices were unsaturated and saturated by the magnetic field. The results showed that capture behavior of the circular and elliptic matrices were magnetic field dependent. The absolute difference of the particle capture cross section area between the circular and elliptic matrices increases first and then decreases with the increase of magnetic induction (0.1-0.8 T). The capture cross section area of the elliptic matrix can be 1.25-1.6 times larger than that of the circular matrix within a moderate induction range. In high magnetic induction, the capture cross section area of the circular and elliptic matrices is almost the same. The analyses provide explanation for the conflict in previous publications and reveal the good magnetic characteristics of the elliptic matrix and its promising application prospect in HGMS.