Magnetic nanoparticles, as controlled drug carriers, provide tremendous opportunities in treating a variety of tumors and brain diseases. In this theoretical study, we used magnetic nanoparticles, such as Superparamagnetic Iron Oxide Nanoparticles (Fe3O4) (SPION). Due to their biocompatibility and stability, these particles represent a unique nanoplatform with a great potential for the development of drug delivery systems. This allows them to be used in medicine for targeted drug delivery, in magnetic resonance imaging and magnetic hyperthermia. In the work, the trapping mechanisms of magnetic nanoparticles moving in a viscous fluid (blood) in a static magnetic field are numerically studied. The equations of motion for particles in the flow are governed by a combination of magnetic equations for the permanent magnet field and the Navier–Stokes equations for fluid (blood). These equations were solved numerically using the COMSOL Multiphysics® Modeling Software.