Abstract The present paper is devoted to an extension of Maysel's formula from the linear theory of thermoelasticity to the geometrically non-linear theory of anisotropic solids and structures. The material description of continuum mechanics is used, and the constitutive equations of St. Venant and Kirchhoff are considered under two circumstances. First, we model the thermally induced deformation of anisotropic solids from an undistorted reference state. This leads to a non-linear integral equation for the thermal deformation, extending Maysel's formula of the infinitesimal theory to the regime of moderately large strains. Secondly, the linearized form of the constitutive relation is used to describe an infinitesimal strain superimposed upon a given, intermediate state of stress in a hyperelastic material of arbitrary type. The intermediate strain needs not be small. It is shown that, when properly interpreted, Maysel's formula may be applied directly to this second case, without any additional terms. The presented results should be of a rather general interest, since they lead to an efficient and powerful representation of the thermal response of anisotropic materials. As a structural application, Maysel's formula is subsequently derived for shear-deformable beams made of a St. Venant–Kirchhoff material. Geometric non-linearity is taken into account according to the assumptions of v. Karman, and the influence of shear is considered in the sense of Timoshenko. A semi-analytic solution procedure is derived for the case of simply supported beams with fixed ends. The thermally induced deflection is derived in closed form, and a non-linear equation is presented for the corresponding normal force. In the post-buckling regime, three branches of the solution are found in the considered range of thermal loading. Thermally loaded beams made of pyrolitic–graphite type material are studied, and the strong influence of the characteristic parameter of anisotropy is demonstrated. Stability of the solution is discussed, and results are compared to finite element computations in the isotropic case. An excellent agreement is found, and a paradoxical behavior of the finite element code abaqus is clarified.