A method for printing and decorating packaging materials, such as paper, paper board and various flexible polymer films by electron beam exposure of plural layers of curable inks and coatings which do not substantially change viscosity during the printing process. The inks and coating are essentially free of volatile components such as organic solvents, inorganic solvents, water and low molecular weight fractions before, during and after exposure to electron beam irradiation. The method involves applying multiple layers of ink and an optional coating onto a substrate. The ink is an admixture of a colorant, and an unsaturated component such that the inks have a maximum of 10% volatile components. Thereafter these layers are simultaneously exposed with electron beam radiation to cause the ethylenically unsaturated components to polymerize or crosslink such that they become dried.