Abstarct: The structural complexity of high-tech industries is often compromised by a combination of thermal, mechanical, and geometric weaknesses. New generation materials and engineering the structure of materials are among the techniques that engineers employ to eliminate these effects. In this Thesis, a comprehensive analysis solution is derived using Lekhnitskii's complex variable approach with the use of general mapping functions, the concept of functionally graded materials (FGMs), and holomorphic functions in the form of Laurent series. This general solution is used for the thermoelastic analysis of perforated functionally graded carbon nanotube-reinforced composite (FG-CNTRC) plates with elliptical hole. Nanocomposite plate is asymmetric due to the arrangement of CNT and is subjected to remote uniaxial tensile loading and constant heat flux. Following assumptions were considered to solve the problem: 1The equivalent single-laxyer plate theory (classical laminated plate theory) is used for FG-CNTRC plate. 2There is no external load on the hole boundary. 3The edge of polygonal holes is considered thermal insulation. 4The FG-CNTRC plate is infinite. 5The Neumann and mechanical boundary condition was considered for the hole and problem. A refined-calibrated rule of mixtures is used to approximate the material property of FG-CNTRC plates according to gradational changes in direction of thickness and available molecular dynamics simulations results. To validate the implemented solution method, compliance with finite element solution results in Abaqus software and results of asymmetric laminated composite elastic analysis has been used. The effect of FG-CNTRC material properties, heat flux condition, and two parameters affecting the shape of the elliptical hole has been investigated. During the present parametric analysis, the results clearly show that the parameters each provide a reliable tool for designers to influence the stress and moment resultants to minimize undesirable stresses. Due to general formulation it is able to calculate thermoelastic parameters (as well as thermal and mechanical parameters, separately) for the generalized problems of the FGM plate or composite laminates with an elliptical hole.