The surveyed problem is relevant today because of the existing discrepancy between the increased need of the society and the government in high quality university engineering education and the real maturity of engineering graduates to perform their professional duties, as well as the insufficiently developed theoretical foundations of student research in the context of competence-oriented education. The purpose of this paper is to solve the problem of forming the research competence of students in the course of independent and scientific research work in the educational process at University of engineering. Based on the systematization and development of existing approaches to the solution of the problem of research training for engineering university students contributing to the development of a functional model, a methodology for the formation of research competence in the course of independent and scientific research work of students of engineering universities is presented. The viability and expediency of creation and work of initiative groups focused on the fulfillment of creative research assignments is substantiated. The process of fashioning practical experience of research activity with the participation of students in scientific seminars is described; the process of using projects method through research tasks in the implementation of coursework, qualification works is presented; fixing and improving the experience of research activities of future engineers during all types of practice is considered.