Sodium hydride is a powerful reduction agent used in chemical industry. Industrial production of sodium hydride through hydrogenation of melt sodium dispersed in mineral oil is very demanding because of the complex multiphase system (liquid-liquid-gas-solid) and safety aspects. A new mathematical model was developed for the production of solid sodium hydride from dispersed liquid-phase sodium and molecular hydrogen. New rate equations were derived for the hydrogenation process of dispersed sodium droplets in a semi-batch reactor. The model comprises surface reactions as well as liquid-solid mass transfer effects of hydrogen. The properties of the differential-algebraic model were investigated by numerical simulations and the model was verified with experimental data of sodium hydrogenation in an isothermal, intensively agitated semi-batch reactor. The kinetic and mass transfer parameters included in the model were estimated successfully with non-linear regression analysis and the model gave a good reproduction of the experimental data. The molecular-level model can be used for the design and optimisation of sodium hydride production processes.