One of the important problems of the methodology of teaching any discipline is the effective identification of the objective level of students’ knowledge, acquired skills and abilities in the study of a discipline. Traditional methods of testing and assessing knowledge contain some drawbacks: excessive time spent on the exam; elements of teacher’s subjectivity that may occur; inability to clarify clear criteria for assessing knowledge, etc. Based on this, and the prospects for the reform of higher education in Ukraine, such methods of knowledge control are needed, which would allow teachers not only to establish an objective level of students’ knowledge, but also to identify (diagnose) the causes of gaps in student learning so that they could on its basis help the student to overcome the identified gaps. This method, devoid of most of the above shortcomings, is computer testing, the use of which for a long time as a means of monitoring and evaluating students’ achievements in studying the course of General Physics and Profession-oriented English at the Department of Materials Science and New Technologies (State higher educational institution "Vasyl Stefanyk Precarpathian National University"), at the Department of Physics and the Department of Western and Oriental Languages and their Teaching Methods (The State Institution“ South Ukrainian National Pedagogical University named after K. D. Ushynsky”) has shown that the use of computer testing in the study of Physics and foreign languages in the professional field should be subject to certain reservations, since this method has some advantages alongside disadvantages that can distort the results of monitoring and evaluation of students’ achievements. Based on the analysis of the authors' experience as well as the analysis of pedagogical, psychological and scientific-methodological literature devoted to this problem, an attempt is made to establish the conditions and limits of computer testing in the organization of the learning platform (courses) in the fields of General Physics and foreign languages for the students majoring in Physics at institutes of higher education. The article states that computer testing, on condition that tests meet the quality requirements, should be used only for the current (thematic) control of knowledge during each semester. This method is at the same time an express control method aimed at testing students' knowledge in the process of studying General Physics and foreign languages; it is also a “sensitive” diagnostic method which allows you to identify shortcomings of a student in time in the process of learning, giving the teacher the opportunity to timely influence its course. The learning progress control (testing in theoretical modules) can be carried out by means of computer testing but with the use of certain additional precautionary methodological measures. It is more expedient to carry out the final control in the form of a quality written-oral examination.