During the last decade the offshore wind industry grew ceaselessly and engineering challenges continuously arose in that area. Installation of foundation piles, known as monopiles, is one of the most critical phases in the construction of offshore wind farms. Prior to installation a drivability study is performed, by means of pile driving models. Since the latter have been developed for small-diameter piles, their applicability for the analysis of large-diameter monopiles is questionable. In this paper, a three-dimensional axisymmetric pile driving model with non-local soil reaction is presented. This new model aims to capture properly the propagation of elastic waves excited by impact piling and address non-local soil reaction. These effects are not addressed in the available approaches to predict drivability and are deemed critical for large-diameter monopiles. Predictions of the new model are compared to those of a one-dimensional model typically used nowadays. A numerical study is performed to showcase the disparities between the two models, stemming from the effect of wave dispersion and non-local soil reaction. The findings of this numerical study affirmed the significance of both mechanisms and the need for further developments in drivability modeling, notably for large-diameter monopiles.