A one-dimensional, magnetohydrodynamic model, in which the Ohmic heating is considered, was proposed to numerically calculate the experiment Z-452 carried out on the Z machine at Sandia National Laboratories. The computed free-surface velocities of the flyer plates agree well with the experimental records by VISAR. The paper also analyzes the ablation induced by the Ohmic heating in the flyer plates and the penetration of magnetic field. The obtained velocity, pressure history curves are helpful to understand the physical mechanism of magnetically accelerated plane flyers.