Although the importance of knowing the magnitude of residual stress (RS) and its functional significance are widely recognized, there is still disagreement and confusion regarding the nature of physical mechanisms giving rise to RS in tissues and organs. Here an attempt is made to examine the various mechanisms which may be involved in producing RS, and to estimate their roles and significance based on previously published experimental observations. Two concepts are introduced. The first establishes a hierarchy of different possible RS producing mechanisms from the micro (local) level of the tissue space, through the meso-level of the whole tissue, to the macro (organ) one. Whereas micro-level RS seem to be present in all soft tissues, the existence of macro- and meso-level mechanisms are tissue and organ specific. The second concept introduced highlights the significance of tissue swelling as an RS producing mechanism in the local micro-level. The implications of RS mechanism hierarchy are discussed regarding the interpretations of commonly used experimental methods aimed to study RS or to estimate its magnitude. Of the three categories of RS mechanisms, the local micro-RS is the least understood. It is analyzed here in terms of the tissue’s multiconstituent structure, in the framework of mixture theory. It is shown that the micro-RS can stem either from interactions between the solid tissue constituents or between its solids and its fluidlike matrix. The latter mode is associated with osmotic-driven tissue swelling. The feasibility of these two mechanisms is analyzed based on published observations and measured data. The analysis suggests that under conditions not too remote from the in vivo homeostatic one, osmotic-driven tissue swelling is a predominant RS producing mechanism. The analysis also suggests that a true stress-free configuration can be obtained only if all RS producing mechanisms are relieved, and outlines a manner by which this may be achieved.