<p>A physical and mathematical model is proposed for determining the components of the stress tensor and stress intensity in an electroconductive strip during its induction heating by a quasi-steady electromagnetic field. A two-dimensional thermomechanical problem is formulated for an electroconductive strip with a rectangular cross section. The determining functions are the tangential component of the magnetic field intensity vector, temperature, and components of the quasi-static stress tensor. To solve problems of electrodynamics, thermal conductivity, and thermoelasticity, approximations of all determining functions in the thickness variable are used with the use of cubic polynomials. This approach reduces the initial two-dimensional problems for these functions to one-dimensional problems containing their integral characteristics. General solutions for integral characteristics are obtained using finite integral transformation in the transverse variable, as well as Laplace transformation in the time variable for electrodynamics and heat conduction problems. Numerical analysis is performed with respect to changes in the components of the stress tensor depending on the dimensionless Fourier time, the Biot number, and the parameter characterizing the relative penetration depth of induction currents. The thermo-stress state of a non-ferromagnetic strip made of stainless alloy steel under conditions of near-surface and deep induction heating by a quasi-steady electromagnetic field is investigated.</p>