The article discusses issues related to the design, development and implementation of the model of adaptive system for mathematical training of students within eLearning environment. It proposes a systematic set of scientific, theoretical and methodological provisions and approaches that determine the design of the model. The research objective of the paper is designing, developing and implementing a model of the adaptive e-learning system for students to improve their mathematical skills. The article gives the definition of the adaptive system for mathematical training of students. It describes the algorithm of adaptive learning of students within the system in the form of a sequence of operations and actions focused on achieving the learning outcomes, including diagnostics and detailing of personal student’s characteristics; designing a student model based on personal student’s characteristics and preferences; differentiation and selection of educational technologies, resources and teaching methods depending on personal student’s characteristics and preferences; formation and provision of an individual learning path to a student; assessment and analysis of student’ performance. In the work the authors used theoretical, empirical and mathematical research methods. The article gives the results of a pedagogical experiment on the use of the adaptive system for mathematical training of students within eLearning environment in the educational process of the higher educational institution, which proves a positive dynamics in the level of mathematical preparedness of students studying within the proposed adaptive system.