Magnetic element is the basic component of matrix in high gradient magnetic separation (HGMS), and its configurative parameters such as size have marked effects on the capture efficiency of the matrix. Therefore, the geometric design of the element should be matched with the properties of the material to be separated, to optimize the HGMS performance. In this work, the capture of independent magnetic particles on a cylindrical element in pulsating HGMS process was theoretically described, and their size matching ratios (magnetic element to particle) under the maximum capture probability and critical capture conditions were specifically discussed. These theoretically calculated size ratios were much larger than that (2.69) in the literatures available, but generally consistent with those obtained from pulsating HGMS applications. The theoretical analysis were basically validated by the actual capture of ilmenite and hematite particles on cylindrical elements, using an experimental magnetic capture method. According to the new theoretical model, the size matching ratio is not fixed at the value of 2.69. It depends on the properties of the material to be separated such as volume magnetic susceptibility and the operating parameters of a HGMS process such as magnetic induction and flow velocity through the magnetic element. This theoretical description provides a new fundamental understanding in the size matching between magnetic element and particle, and would contribute to the solution of size matching issue in the real capture situation considering the interactions between magnetic particles, and therefore to the optimal design and operations of matrix in HGMS applications.