Prospects for Applied Mathematics and Data Analysis PAMDA 2836-4449 10.54216/PAMDA https://www.americaspg.com/journals/show/1839 2022 2022 Department of Mathematics, AL Baath University, Homs, Syria Mountajab Al Al-Hasan The importance of results of this paper consist in supplying new analytical method for solving the Ignaczak tensorial equations, governing the thermodynamical plane state of small elastic strains of the homogeneous, isotropic, micropolar elastic solid of 5 material constants of Eringen-Nowacki type, which shortly called  2D (E-N:5) (Iron plates, copper plates, aluminum plates, .. etc.).  The paper covers the mathematical model of the first plane state of small elastic strains of micropolar homogeneous and isotropic solid, of five material constants, subjected to temperature field, mathematically proposed by Eringen and Nowacki, and shortly called 2D (E-N:5).  In paper, for the 2D (E-N:5) considerable body, we generalize the Schaefer vector method to: I) The Traditional Description of the 2D (E-N:5) considerable body, II) The Ignaczak Description of the 2D (E-N:5) considerable body. Subsequently, these results have important applications in material resistance, plate theory, industry ….etc.     2023 2023 27 41 10.54216/PAMDA.020103 https://www.americaspg.com/articleinfo/34/show/1839