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We describe an analytic-numerical method of solution of one-dimensional static thermoelasticity problems for layered plates, heated in different ways. We take into account the cubic dependence of the coefficients of heat conductivity and arbitrary nature of the dependence of other physicomechanical parameters on temperature. Here, using the constructed exact solution of an auxiliary problem, we have reduced the heat conduction problems, irrespective of the number of layers, to the solution of one or a system of two nonlinear algebraic equations. We have also studied the temperature fields and stresses in four-layer plates under conditions of complex heat exchange.The determination of the thermoelastic state of both homogeneous and inhomogeneous bodies, in particular, those with plane-parallel boundaries, with regard for their thermal sensitivity (the dependence of physicomechanical characteristics on temperature) has attracted the attention of numerous researchers [4,[15][16][17][18][19][20]. Even in the case of uncoupled thermoelasticity problems, the corresponding heat conduction problems remain nonlinear. For their solution, it is customary to apply the Kirchhoff substitution [1, 2, 5, 6, 9-12, 14, 16]. This technique enables one to linearize the problems under study partially or even completely and, correspondingly, to simplify their solution or, in some cases, to obtain an exact solution. However, for layered bodies, one does not succeed in completely linearizing heat conduction problems, including the simplest, one-dimensional, because nonlinearity is preserved in one of the conditions of thermal contact. Obviously, the solution of heat conduction problems and, hence, of the corresponding thermoelasticity problems becomes more difficult both in the case of convective or convective-radiative heat exchange with the environment and taking into account more complex temperature dependence of the coefficients of heat conductivity than linear. Therefore, such problems are solved, as a rule, by numerical and approximate analytic methods or by their combination.In the present work, we describe an analytic-numerical procedure, based on using the approach [7], of the solution of one-dimensional static thermoelasticity problems for layered plates, heated in different ways, with regard for the cubic dependence of the coefficients of heat conductivity and arbitrary character of the dependence of other physicomechanical characteristics on temperature. Using the exact solutions of the corresponding equations under special boundary conditions, constructed with the help of the Kirchhoff substitution and generalized functions, we reduce the heat conduction problems under study, irrespective of the quantity of layers, to the solution of one or a system of two nonlinear algebraic equations. The thermoelasticity problem is solved in terms of stresses. The boundary conditions on the cylindrical surface are satisfied integrally. We also analyze numerically the temperature fields and thermostressed state in four-layer plates under ...