The numerical simulation of pile driving presents numerous challenges because it comprises several non-linearities: geometric no-linearity due to the large deformations, material non-linearity associated with the plasticity of the surrounding soil and contact non-linearity arising from the interaction between the soil and the pile. Therefore, special numerical methods are needed to model the pile installation process. Among the various numerical methods available to model large deformation problems, the Geotechnical Particle Finite Element Method (G-PFEM) has proven to be a successful tool for the simulation of insertion problems in geomechanics [1]. The G-PFEM is a specific implementation of the original Particle Finite Element Method [2], which uses low order stabilized finite elements and includes coupled hydromechanical formulations for quasi-static and dynamic conditions. In this work, the G-PFEM is used alongside a critical state-based constitutive model that considers the effects of the initial density on the strength and compressibility of sandy soils. Following a large deformation approach, the model is formulated using a hyperelastic model and a multiplicative decomposition of the deformation gradient into an elastic and plastic part. The effectiveness of this numerical approach is demonstrated by simulating the installation of an open-ended pile in dry silica sand using monotonic jacking and hammering. The results are compared with the penetration resistance and blow count recorded in the centrifuge test performed by Fan et. al. [3]. Furthermore, the results of the hammering installation are compared with the state of the practice driveability analysis using one dimensional wave propagation analysis. The findings demonstrate that the G-PFEM can adequately simulate the process of pile driving, and the selected constitutive model allows considering the effect of the modification of the soil state during pile installation. Moreover, the results highlight the benefits of using advanced numerical simulations in contrast to simplified approaches such as the wave equation analysis to obtain more accurate estimations of pile driveability.