Diffusion of elements and vacancies is embedded in the framework of continuum mechanics and thermodynamics. The evolution equations for the site fractions of the substitutional and interstitial elements as well as the vacancies are derived. Each possible activity of vacancies, from no to non-ideal and ideal sources and sinks for vacancies, is taken into account. Manning's theory is implemented considering the vacancy wind effect. Furthermore, the role of a stress state is rigorously treated and shows its different influence on substitutional and interstitial elements as well as on vacancies. The reader is provided by the full set of diffusion equations for each kind of vacancy activity. Physically most relevant types of boundary condition, representing closed system with different activities of vacancies at its surface, are studied in detail. The theoretical framework is demonstrated by two illustrative examples emphasizing the interaction of bulk diffusion with an internal phase interface and/or the surface of the system expressed by contact conditions taking into account the properties of the interface or the surface. (C) 2013 Elsevier Ltd. All rights reserved.