Monopiles are by far the most chosen foundation option for most off-shore activities. The installation of the foundation is commonly done by impact pile driving. The biggest issue of the traditional pile driving method is the sound emission, which reaches levels that are harmful to the immediate environment. Partly because of this, an alternative pile driving method is being developed, namely the Gentle Driving of Piles [1], where the hydraulic hammer is replaced by a GDP-shaker, which drives the pile toe into the ground by means of a torsional force. This is an additional incentive for developing a predictive model for the underwater noise radiation due to a non-symmetric force field. The model proposed in this thesis is similar to the existing symmetric semi-analytical model SILENCE [2], where the model consists of two submodules, namely a pile module and a module that describes the acousto-elastic medium. In both submodules the displacement field of the subsystem is described using its modal field. The procedure for both systems are derived and explained in further detail in chapter 3. To combine the submodules two different mode-matching methods, that account for the azimuthal direction, are developed in chapter 4. One of these methods is the so-called Orthogonality method, which is, similar to [3], based on the orthogonality relations of the acousto-elastic medium. The other is referred to as the Point-Collocation method, which is loosely based on the reciprocity theorem. Both methods have proven to be sufficiently stable to achieve good convergence at least for lower frequencies. The model is tested a small sized pile case study. The results are assessed in chapter 5 through the frequency spectra of the acousto-elastic medium as well as the metrics. The time evolution of the response is also looked at, even though these are considered less reliable, due to the limited frequency range.