The article contains an attempt to reveal the qualitative characteristics of programmed instruction by the method of mathematical modelling, in particular by applying some of the basic pieces of knowledge from the theory of abstract automatons. Viewed from this angle, programmed instruction is understood as an interaction of two systems, the learning system (pupil, student), which can be imagined as a stochastically determined automaton, and the teaching system (textbook, teaching machine), which can be imagined as a determined automaton, being determined by the educational aim and the content of the programmed teaching material. The next part of the article is devoted to a structural analysis of a branching programmed textbook of „the Divisibility of Natural Numbers“ from the position of these teaching automatons. The program studied is described by the incidence of inputs and outputs of individual pages and the learner’s attainment is described by the dynamics of information in individual branches. In conclusion it is stated that as for practical use of mathematical modelling of instruction from a branching programme, it brings a number of new indexes and methods suitable for assessing the effectiveness of teaching and as for theory it brings a number of new pieces of general information about the educational process.