<p>The flow of a non-Newtonian Jeffrey fluid over a pulsating plate in a rotating frame is analysed. The effects of the Coriolis force and a constant magnetic field are also studied. The velocity of the plate is periodically pulsed, while the remaining part of the rotating fluid exhibits unsteady motion. Exact solutions for each case are obtained using the Laplace transform method with Mallin’s integral inversion formula. The graphical analysis shows how rotation, elasticity and magnetic field influence the fluid velocity during plate pulsation. It is found that the longitudinal component of velocity decreases with higher values of the Jeffrey parameter and magnetic field, while the transverse component of velocity shows the opposite behaviour.</p>