Nonlinear soil–pile–structure interaction (SPSI) phenomena are known to play a vital role in the response of bottom-fixed marine structures. For such structures, these phenomena are commonly considered by the imposition of p-y, τ-z, and q-z springs, representing the lateral and axial shaft and axial base soil resistances, respectively. The importance of each resistance mechanism depends on the type of foundation system, with only very limited studies investigating their roles in the response of piled marine structures, such as jetties. Within this context, this study presents numerical three-dimensional pushover analysis results for two marine jetties, a smaller model with four piles and a larger model supported by twenty-four piles. SPSI effects are considered through p-y, τ-z, and q-z springs, the behaviours of which are determined by following commonly employed procedures. The structures’ responses are investigated under the influence of various assumptions regarding the behaviours of springs, as well as steel plasticity. The current investigation underscores the substantial influence of the axial soil–pile interaction on the response of the jetty, particularly in terms of its failure mode. Moreover, it demonstrates the importance of incorporating p-y springs, even though the choice between their linear or nonlinear constitutive behaviour is found to be less critical. Finally, the study concludes that the behaviours of the springs significantly affect the system’s ductility and the degree of steel yielding in the piles, while also highlighting the unconservative influence of neglecting SPSI phenomena.