The article deals with an extremely important problem of teaching technical department students to work with science texts in foreign language.The main areas of researches devoted to reading psychology problems and psychological readiness are examined. In the introduction the author justifies the importance of foreign languages learning in formation of technical department students and the role of the teacher in their motivation to read science texts and to overcome cognitive difficulties during reading. As scientists frequently use a specific, mathematical language, with symbols and formulas that are difficult to ground in everyday experience and that often require extreme precision a teacher must learn students to be ready for these difficulties and to overcome them.The author gives proof of creating of practical course that would improve reading and comprehension skills. It is also very important to take into account such individual psychological features as multiple intelligence, learning style of each student and so on.The components of psychological readiness of students to work with foreign science texts that influence their comprehension are described. The author presents the objective of the Foreign Language for Specific Purposes lessons, aimed at creating a psychological readiness of students to the work with foreign science literature; knowledge, skills and experience that should be formed and developped on these lessons. They predicted the results of testing these FLSP lessons.