The classical two-dimensional biharmonic problem for a rectangular domain is considered. Some historical aspects of the problem are elucidated. The superposition method turns out to be efficient in solving thermoelastic-equilibrium problems in a rectangle. The relationship between the mathematical and engineering approaches to these problems is studied. A few typical examples are given Keywords: biharmonic problem, thermoelastic stresses in rectangle, infinite systems of linear algebraic equations Introduction. Nowadays, the needs of technology provoke interest in thermal-stress problems for various structures. Thermal stresses in structural members were intensively studied in the mid-20th century because of important practical problems that arose in designing new steam and gas turbines, jet and rocket engines, and nuclear reactors [1,6]. Members of such structures are subject to nonuniform and often nonstationary heating that causes temperature gradients and unequal thermal expansion of isolated components. Such nonuniform thermal expansion cannot proceed freely in an elastic body and induces thermal stresses. The magnitude and behavior of thermal stresses must be known to allow comprehensive strength analysis of structures.Thermoelasticity became an independent division of elasticity theory quite a long time ago-linear equations incorporating the thermal effect were derived independently by Duhamel [47] and Neumann [68]. In these fundamental works, they not only set up the governing equations of thermoelasticity, but also solved elementary one-dimensional problems for thermal stresses. The general formulation of the stress problem was discussed in the recent publications [42,43]. Thermoelastic problems were addressed in fundamental courses on elasticity theory due to S. P. 15, 16, and drills therein] and in fundamental treatises due to A. E. H. Love [23, Sect. 74], N. I. Muskhelishvili [31, Sect. 62], and A. I. Lur'e [ 22, Ch. 1, Sect. 13, Ch. 3, Sect. 7, Ch. 4, Sect. 4]. Moreover, these problems were discussed in monographs of Soviet and foreign authors [1,6,12,13,21,24,26,32,34], which include detailed bibliographies on the subject. In this variety of publications, A. D. Kovalenko's textbooks [14,15,17] stand out due to their concise format, clear formulations of problems and methods of their solution, wide coverage of almost all divisions of static and dynamic thermoelasticity, and in-deep analysis of the possibilities for practical application of results. It is not surprising that the first textbook was translated into English [54].It is often possible to analyze the thermostressed state of an elastic body under plane-strain conditions: the plane strain of an extended body of constant cross section where thermal processes do not depend on the longitudinal coordinate and (generalized) plane stress state of a thin, simply connected, isotropic plate of constant thickness. Two-dimensional quasistatic problems of thermoelasticity for a known temperature field and no surface mechanical loads on the boundary of t...