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In this study we used a Boundary Integral Method to solve the following three problems of uncoupled, linear Magnetoelasticity and Magneto-thermoelasticity: 1)- an infinite, elliptical cylinder carrying a steady, axial, uniform electric current, in the presence of an external temperature. 2)- an infinite, elliptical cylinder subjected to an external, transverse uniform magnetic field. 3)- two infinite, parallel, circular cylindrical conductors carrying steady, uniform, axial currents. The aim of the work is twofold: to assess the used boundary integral method for efficiency, and to investigate some problems of practical interest, in which different fields interact.