Controlled Modulus Columns (CMC) are an increasingly popular ground improvement technique based on column inclusions, due to their simplicity and construction efficiency. CMC are installed using a displacement auger by displacing soil laterally around the column. However, the installation process induces significant soil deformations and complex nonlinear behaviour, posing challenges for numerical modelling. When such large deformation problems are simulated in conventional small-strain finite element programs severe mesh distortions often arise due to the extensive soil displacement, compromising the accuracy and stability of the analysis. This study employs the Coupled Eulerian-Lagrangian (CEL) approach available in ABAQUS/Explicit to simulate the CMC installation process. The Modified Cam-Clay constitutive model is adopted to represent the realistic behaviour of clay soils. The analysis focuses on evaluating the load-bearing capacity of the columns and the influence zone around the column by examining changes in horizontal stress. Additionally, the evolution of excess pore water pressure during installation is investigated.