In this paper, a two-dimensional (2-D) Finite Element (FE) analysis of a geothermal well was performed with respect to five different cross-sections corresponding to the design specifications for the geothermal well that is currently constructed in Pohang, South Korea. Among the essential components (such as ground formation, casing, and cementing) of a geothermal well, the thermal and mechanical stability of the cementing component was discussed based on a series of parametric studies with consideration of the thermal conductivity and Young’s modulus of the cementing component. With increasing number of casing layers, the cementing component experiences less stress concentration. In addition, the lower thermal conductivity of the cementing material is advantageous for effectively controlling radial displacement. Consequently, it should be noted in geothermal well cementing construction that long-term strength degradation of the cementing might cause the severe structural instability of an entire geothermal well.