The paper provides statements and solution procedures for static and dynamic problems for layered shells taking into account the phenomena occurring at the interfaces during the joining of layers (interlayers (ILs)). A unified method for solving the problems is proposed. It is based on the virtual-displacement principle (VDP), which allows an effective description of discontinuous mechanical characteristics and force fields. Systems of ordinary differential equations for amplitude coefficients are derived using the VDP for layered cylindrical shells with ILs. The constitutive equations are represented in explicit form for arbitrary coordinate functions, various types of end conditions and loads. Formulas to determine the strains in layers and physical and mechanical characteristics of ILs based on the mixing rule are given. A general approach to determining the stress state of ILs is outlined Keywords: layered shell, virtual-displacement principle, interfacial phenomena, interlayer, mass concentration 1. Introduction. The theory of layered plates and shells (layered systems) is a well-developed branch of solid mechanics. This area of knowledge includes various theoretical developments, solution procedures, and a great number of research papers and monographs [1-3, 5, 8, 11-16, etc.].In considering such mechanical objects, the question arises of how layers can be joined to produce a continuum system. The statements of many solved problems usually disregard this question.This question deserves attention because of the following. In some cases, the contacting surfaces of a layered system are chemically and thermodynamically nonequilibrium systems usually in air or, generally, in gas.As a result, at the interface between layers, where chemical and diffusion phenomena occur, there are layers of a different material-interlayers (ILs). It was established in numerous studies [6, 7, 9, etc.] that these interlayers are vital for the strength and integrity of a layered system.Of interest is how the formation of an interlayer can be qualitatively and quantitatively described on the grounds of continuum mechanics, how its mechanical properties can be determined, how the available theoretical developments on the mechanics of layered systems can be extended to allow for the presence and influence of an IL, and what design models should be used to analyze the stress-strain state (SSS) at an arbitrary point of the system, including the IL. Note that ILs may result from processes of joining by means of, for example, various solders, glues, adhesive films, etc.It should be noted that stress-strain analysis of layered elements is possible when the thickness, physical and mechanical characteristics, and adhesive and cohesive parameters of ILs are known. Design of layered systems with known geometrical, physical, and mechanical characteristics of ILs will be called the first class of problems of the mechanics of layered systems with ILs. A more difficult problem arises when ILs are formed at high temperatures and pressure (for example...