Magnetic microbubbles (MMBs) can be controlled and directed to target site by a suitable external magnetic field, have potential in therapeutic drug-delivery application. However, few studies focus on their dynamics in blood vessels under the action of magnetic and ultrasonic fields, even little insight into mechanism generated in diagnostic and therapeutic application. In this case, equations of MMBs were established for simulating translation, radial pulsation and the both coupled effect. Meanwhile, the acoustic streaming and shear stress on vessel wall were also presented, which are associated with drug release. Results suggest that the magnetic pressure increases bubble pulsation amplitude, and the translation coupled with pulsation are manipulated by magnetic force, causing the retention in target area. As the bubble approaches the vessel wall, the acoustic streaming and shear stress increase with magnetic field enhancement. Responses of bubble to a uniform and a gradient magnetic field were explored in this work. The mathematical models derived in this work could provide theoretical support for experimental phenomenon in literature and also agree with the reported models.