A method for multicolor printing of stock in web or plate form and having a smooth, nonabsorbent surface, includes printing on the stock by the indirect flexographic printing process; assigning each color to be printed to a respective printing unit which includes an inking unit, a cylinder for a flexographic printing form, a transfer cylinder and a counterpressure cylinder; always drying the ink on the stock before passing the stock to the next printing unit; and removing ink located in indentations and on sides, respectively, of the printing surfaces of the flexographic printing form; and a printing press for printing in accordance with the method.