A mechanical model is suggested herein to explore the interaction between a boulder and a pile being driven, taking into account the properties of the rock forming the boulder and the embedding geological formation. A one-dimensional model is considered as a first attempt, with a view to integrate it into a classical one-dimensional wave-equation representation of the pile being driven. A typical case of a tubular pile driven into stiff glacial till by a hydraulic hammer is investigated. The proposed model is shown to highlight the influence of pile dimensions, boulder size, and hammer energy on the potential damage to the pile toe. Conclusions can be drawn in terms of an optimal range of hammer operational setting, depending on expected boulder size.