Nowadays there is a tendency of the growth of applied problems for the solution of which formal methods and computers are used. Naturally, there arise problems of correspondence between theory and practice, the key one being the assessment of the quality of the obtained results. The paper deals with questions of management of the applied problem solution. Three groups of problems have been considered. The problems concern the formalization, selection and construction of the model, method and algorithm of the solution as well as the justification of the obtained results. Features for characterizing the class of applied problems have been determined. General principles of the transition from the meaningful description of a problem to its formal statement have been proposed. Main methodological aspects of the problem solution have been singled out. The result justification scheme, based on the inductive nature of problems, has been proposed. All the fundamental notions and results are exemplified by applied problems from pattern recognition and artificial intelligence.