Introduction. Solving the problem of heat transfer in multilayer structures devoted a large number of works. The vast majority of them are limited to the case of perfect thermal contact between the layers. However, according to the authors, the problems of thermal conductivity in multilayer structures using into account the imperfect thermal contact are insufficiently studied. The number of such studies is quite limited. Also, known studies are usually limited to two layers. That is because the increase in the number of layers (given the choice of methods of practical implementation) leads to several computational difficulties. Therefore, the problem of constructing an effective analytical scheme for the study of heat transfer processes in multilayer structures in the presence of imperfect thermal contact between the layers remains an urgent task.Purpose. Application of the direct method to the study of heat transfer processes in the system "continuous cylinder inside a multilayer cylindrical shell" with imperfect thermal contact.Methods. An auxiliary problem set for the distribution of the temperature field in a multilayer solid cylindrical hollow body (a cylinder of the sufficiently small radius is "removed") taking into account the imperfect thermal contact between the individual layers. According to the already known scheme of the direct method solve this problem.Results. Boundary transition obtained the solution of the original problem. Boundary transition: the radius of the"removed" cylinder, with the centre at the origin, goes to zero. This approach established that the solution to the problemis limited in the whole structure. In this case, the solution obtained explicit formulas.Conclusions. Effective analytical scheme constructed for application of the direct method to the study of heattransfer processes in multilayer hard cylindrical solids taking into account the non-ideal thermal contact between thelayers. The number of layers, their size and arrangement are considered arbitrary.