An apparatus and method for carrying out the affinity separation of a target substance from a test medium operates by mixing magnetic particles having surface immobilized ligand or receptor with the test medium to promote affinity binding reaction between the ligand and the target substance. The test medium with the magnetic particles in a suitable container is removably mounted in an apparatus of the present invention and magnetic field gradient is created in the test medium. This gradient induces the magnetic particles to move relative to the test medium, thereby effecting mixing. Depending on the embodiment employed, the mixing is achieved either by the movement of an electromagnet or a permanent magnet relative to a stationary container or the movement of the container relative to a stationary magnetic source. After sufficient time for the affinity reaction to occur, the movement of the magnetic gradient is ended, whereby magnetic particles are immobilized on the inside wall of the container nearest to the magnetic source. The remaining test medium is removed while the magnetic particles are retained on the walls of the container and the test medium or the particles subjected to further processing.