A sorting machine (1) for sorting flat articles (100, 101) having non-uniform physical characteristics, the sorting machine having sorting outlets equipped with stackers (3) controlled by a monitoring and control unit in compliance with a plurality of programs, each of which is assigned to a predefined type of flat article (100, 101) having predetermined physical characteristics and setting predetermined operating parameters such as, in particular, the pitch between said flat articles (100, 101), and the speed at which said flat articles (100, 101) are conveyed, the sorting machine (1) having means for determining the predetermined physical characteristics of each incoming flat article (101) arriving in said stacker (3), said monitoring and control unit being arranged to act after said determination to assign a predefined type of flat article to said flat article (101) arriving in said stacker (3) and to activate the corresponding unstacking program so as to apply predetermined operating parameters while said incoming flat article (101) is being stacked.