An analysis is presented of magnetic bead separation in a microfluidic system with integrated magnetic functionality. The system consists of a flow cell on a substrate that contains an embedded array of passive soft-magnetic elements. The elements become magnetized in the presence of an applied field and produce a force that separates the beads from the flow as that pass through the microchannel. In this paper, bead capture is analyzed using a model that combines numerical transport analysis with closed-form field analysis. Particle and fluid transport are predicted using computational fluid dynamics (CFD), while the magnetic force that governs bead capture is obtained in closed-form. The CFD analysis takes into account coupled two-way momentum transfer between the beads and the fluid and the model is used to quantify the impact of this coupling on both the capture efficiency and distortions of flow velocity field. The model is demonstrated via application to a microfluidic system, and the analysis demonstrates that it predicts important aspects of bead transport and separation that are not observed using more conventional one-way coupling analysis, especially for applications involving high particle loading and/or low flow rates. The model presented here is computationally much more efficient and accurate than purely numerical models and should prove useful for the rational design and optimization of numerous magnetic particle-based microfluidic applications, examples of which are also discussed.