Among many alternative building materials, soil in the form of rammed Earth is the most ancient construction material and technology. Large-scale application of the rammed Earth technology in the construction industry requires the assessment of its strength and failure behaviour. Therefore, this study focused on performing a nonlinear stability analysis of cement-stabilized rammed Earth (CSRE) specimens having a height-to-thickness (H/T) ratios—3 and 4 and loaded under varying degrees of eccentricities 0, 1/3, 1/6, and 1/12. The maximum compressive strength and the stress-strain behaviour of the CSRE specimens were determined through finite element (FE) modeling. The experimental results of the cement-stabilized rammed Earth (CSRE) have been obtained from literature for validation by FE simulation. As the H/T ratio was increased from 3 to 4, the load-bearing capacity of the CSRE specimens increased by 2.91% under concentric loading condition; however, when the eccentricity of load application was swapped from 0 to 1/12, 1/6, and 1/3, the load-bearing capacity decreased incrementally. The results of the FE analysis of the specimens showed that the compressive strength and elastic properties of the CSRE specimens did not differ significantly. The stress-strain relationships were nonlinear and elastic properties were affected by soil textural composition and density.