We analyze a magnetothermoelastic problem of the conducting circular plate which is subject to sinusoidal time variation of magnetic flux in the thickness direction. We obtain the analytical solutions of eddy current density, temperature change, displacement, and stresses in the plate under the plane axisymmetric condition. Performing numerical calculation, we discuss the effects of the frequency in magnetic flux and relative heat transfer coefficients at boundary surfaces on temperature change, displacement and stresses of the plate.