Imposition of oscillation electromagnetic force during the solidification process has been expected to be an excellent technique to produce finer solidified structures. An alternating current and a static magnetic field are imposed to liquid metal in mutually orthogonal directions to generate oscillation flow driven by an electromagnetic force near solidification interface. It was reported that dendritic structures were experimentally changed into fine equi-axed structures by imposition of the electromagnetic oscillation under some particular conditions, however necessary conditions for such refinement by the electromagnetic oscillation have not yet been specified. In order to apply this technique to a real industrial process, mechanism of refinement by the electromagnetic oscillation should be understood, and suitable conditions to achieve effective refinement should be clarified. In the present study, theoretical solutions of oscillation flows driven by the electromagnetic forces were analyzed. It was found that the flows through dendrite primary arms could be characterized by several dimensionless parameters such as oscillation Stuart number,Nω, shielding parameter, Rω, Womersley number, Wo1, Reynolds number, Re1, and Péclet number, Pe1. Required conditions for refinement by the electromagnetic oscillation were investigated and estimated as follows: Nω<<1, Rω>>1, Wo1≥1, Re1>>1, Pe1≥1. The result corresponds reasonably well with the experimental date in previous research.