A continuum model of dendritic solidification of multicomponent alloys is used to predict the volume fraction of porosity caused by precipitation of hydrogen gas during solidification of A356 aluminum plate castings. The conservation equations of mass, momentum, energy and species transport are solved to simulate the transient solidification process, including thermosolutal convection and segregation during the formation of the mushy zone. The amount of hydrogen supersaturation is calculated based on the transport of dissolved hydrogen and Sievert's law. An innovative aspect of this work is the extension of the model to make quantitative predictions of the volume fraction of porosity. Although the hydrogen supersaturation has been used in previous works to estimate the amount of porosity, these predictions are usually grossly overestimated, because the barrier of pore nucleation is not considered. In this work it is shown that it is possible to make good estimations of the volume fraction of porosity by combining the hydrogen supersaturation with the calculated local solidification times. Computer simulations are performed in plate castings, showing good qualitative and quantitative agreement with experimental data.