The article focuses on the application of tasks containing a variable under the sign of the module in problems of mathematical olympiads. The results are obtained: the topics of the section are determined, on the basis of which the conditions for the olympiad problems of the republican olympiad are compiled, the goals and requirements for studying the absolute value in the olympiad program are determined, 5 main methods for solving equations with a module are identified: methods for sequentially opening modules, intervals, graphical, determining the dependencies between numbers a and b, their modules and squares, geometric interpretation of the module. In the course of the study, conclusions were drawn: due to the increasing complexity of the olympiad problems, there is a need to familiarize students with different methods for solving the olympiad tasks with a module in the system of additional education.