The importance of “soft skills” for teaching activities is increasing every day. The concept of “soft skills” has been actively developed in Western pedagogical science since the beginning of 2000, in domestic science, a single approach to the interpretation of “soft skills” does not exist and, on the whole, rather limited attention is paid to this problem. Western and Russian scientists include the following components in “soft skills”: emotional intelligence, persuasion, finding an approach to people, communicative and managerial talents, ability to resolve conflict situations, preparedness for thoughtful risk, stress, stress and conflict, creativity, flexibility, inclination to finding alternative solutions. Most researchers consider the professional stability of teachers as an integrative quality of personality, as a key component of the teacher’s professional culture, as the stability of emotional reactions, the ability to regulate the emotional state, as a factor of successful professional activities in extreme situations. We understand this term as an integrative quality of a person, ensuring the ability of a teacher to carry out professional activities for a long time with a high level of emotional stability, productivity and efficiency in dynamically developing and extreme situations. The study was carried out on the basis of the Professional Pedagogical Institute of the South Ural Humanitarian Pedagogical University. The study involved 120 bachelors, 52 undergraduates and 27 teachers. Our empirical study has led us to the following conclusions: 1) most subjects of pedagogical activity are not familiar with the term “soft skills”, although when they become familiar with it, they consider it important for their future professional activities; 2) the majority of respondents is familiar with the term “professional sustainability” and considers it important for their professional activities. Also, the majority of respondents consider professional sustainability to be an important “soft skills” of teachers.