In present work we have developed a theoretical model for the description of the electrochemical discharge process in the metal hydride anodes of the metal hydride batteries at various current densities. The model is based on the description of the assembly of the spherically shaped metal hydride particles where the process of electrochemical discharge is fit using a shrinking core model, with a shell of the H storage alloy growing inside the particle by decreasing volume of the internal metal hydride core. The model accounts results of the D.O.S. calculations for La2MgNi9 intermetallic alloy and has been tested for this metal hydride anode material having an electrochemical discharge capacity of 400mAh/g and hydrogen storage capacity of 13 at.H/f.u. La2MgNi9. It allows to quantitatively describe kinetic behaviors of the electrode at various applied current densities and to estimate the diffusion coefficient for hydrogen and equilibrium content of H in the solid solution domain of hydrogen in La2MgNi9. This model has a general applicability and can be used for the optimization of the materials and the electrodes of the metal hydride rechargeable batteries at high current densities.