All SYSTEM/360 functional characteristics having programming significance are completely and concisely described. The description, which is formal rather than verbal, is accomplished by a set of programs, interacting through common variables, used in conjunction with auxiliary tables. The language used in the programs involves operators and notation selected from mathematics and logic, together with additional operators and conventions defined to facilitate system description. Although the formal description is complete and self-contained, text is provided as an aid to initial study. Examples to illustrate the application of the formal description are given in an appendix.