A Mathematical Olympiad is a competition aimed at discovery of gifted students with a remarkable talent for mathematics, increasing their motivation for studying mathematics and developing their research skills. This event enables the teacher to improve their teaching methods and gain more working experience. The article deals with the importance of Mathematical Olympiads for the Ukrainian system of secondary education and highlights peculiarities of conducting all-Ukrainian and International Mathematical Olympiads in stages. The work analyses tasks of the 3rd and 4th stages of all-Ukrainian Mathematical Olympiads between 2015 and 2017 in order to identify the number of theoretical and numerical tasks as well as the most often used theoretical and numerical facts and methods to perform them. Based on this analysis, a conclusion is drawn that theoretical and numerical problems represent a necessary component of each stage of Olympiads, so training 7 to 11 Year students in theoretical and numerical problems is compulsory during students’ preparation for Mathematical Olympiads.