Based on the approach to the rational control of engineering systems in conditions of uncertainty, created by Professor A. Kulik, models and methods of adaptive computer support of getting knowledge and skills in algorithmic academic tasks solving were developed. There were proposed three modes of such systems functioning: demonstration, solving with hints and test, which organized in two stages of training: calculations according to certain algorithm and algorithm development according to certain task statement. The models of algorithmic academic task, the method of calculation and generation of the tasks statements variants, the student model, the method of automatic generation of diagnostic models of missing operands, the data model, the model of teaching and methods of trainee program diagnosis are described in the paper. Proposed models and methods allow to structure and formalize training process, as well as to improve such algorithms characteristics as occupied memory and calculation time in order to provide adaptive computer support of tutoring.