Courses of English for special purposes (ESP) tend to focus on fostering communication skills applied to future professional spheres. These skills are the backbone of soft and employability skills, being on the top target list of the university education at large. Although, soft skills alignment with university curricula throughout the world is the state of the art for now, in Russia, the shift towards soft skills is only at the outset. The literature review of soft skills prompted the authors to single out indisputable soft skills (communication skills including oral communication, written communication, presentation skills; social skills - interpersonal communication, team work, leadership skills; cognitive skills - information skills, critical thinking, problem- solving, and mixed soft skills (mainly related to personal attributes and emotions).With foreign languages, being the most efficient discipline to nurture soft skills, the present research was fulfilled to find out the exposure of ESP course books at Russia's universities to soft skills. The ESP coursebooks were sampled through an ESP experts' selection with limitations to QS universities in Russia; levels B1-C1; courses for bachelor and master students; full-fledged ESP textbooks (full field coverage); Russian authorship. All exercises were grouped to limit the study to those related to soft skills. The research encompassed two (one structured, one Likert-type) questionnaires to get lecturers' and students' assessments of relation of the ESP exercises to the selected soft skills.The findings show that with a bias towards drill-like exercises as a weak point in almost all sampled textbooks, there are exercises and tasks successfully imparting soft skills and developing students' communication and professional language aptitude.