Dynamic compaction (DC) is vastly utilized to improve the strength characteristics of the soils. To predict the soil deformations derived from the DC operations, usually numerical simulation analysis is applied. For the conduction of such simulations, several numerical approaches with different elemental formulations can be used. From the perspective of finite element analysis (FEA), there are four main formulations including the Lagrangian, Arbitrary Lagrangian-Eulerian (ALE), Coupled Lagrangian-Eulerian (CEL), and Smoothed Particle Hydrodynamic (SPH). In this research, a comparative study has been conducted to evaluate the computational efficiency of those four approaches in the prediction of soil large deformations during the DC operations. To do this, for a DC operation executed in a road embankment construction project in China, the real field data was compared to the results obtained from the numerical simulations via the ABAQUS program. The findings demonstrate that of all those approaches, the Lagrangian approach delivers the minimum accuracy of the predicted results, albeit with the least running time. In contrast, the ALE formulation predicted closer estimations of soil deformations although it was found to be less time-efficient. Interestingly, the CEL and SPH approaches predicted the soil deformations with the maximum degree of accuracy whereas they were not as time-efficient as the Lagrangian approach. To address this issue, a hybrid model of Lagrangian and SPH formulations was constituted to satisfy the maximum accuracy with the minimum running time. Such a hybrid model is highly applicable for the accurate prediction of soil large deformations during the DC operations.