Frost is generally detrimental to the efficiency of refrigerated transport systems. To predict the frost growth on a flat cold plate, a Eulerian-Eulerian multiphase model is employed based on a non-dimensional phase change driving force with a frosting criterion for the velocity and water vapor concentration. This model allows for the local frost formation (increase of frost thickness and weight with time) and the humid air flow characteristics to be simultaneously simulated. Densification occurs as an increase in frost thickness faltering with time while the weight continues to increase until the equilibrium temperature is reached at the surface of the frost layer. The velocity of the humid air is near zero at the frost surface and, away from the frost layer surface, it increases as the frost layer thickness increases. The model is favorably validated against published experimental results for both the frost thickness and density.