In urban areas, engineers often need to assess tunnelling-induced displacements of piled structures and the resulting potential for damage. This paper presents an elastic study of tunnel-pile-structure interaction through Winkler-based Two-Stage Analysis Methods (TSAMs), focusing on structural displacements resulting from tunnel excavation beneath piled frames or simple equivalent beams. Comparison of results with 3D finite element analyses shows that the simple TSAM models are able to provide a good assessment of tunnelling-induced building displacements. Parametric analyses highlight the role of tunnel-pile interaction and the superstructure (stiffness, configuration, and pile-structure connections) in the global response of the tunnel-soil-building system. In particular, the effect that key parameters have on deflection ratios and horizontal strains are investigated. Results illustrate how piled foundations increase the risk of structural damage compared to shallow foundations, whereas structural stiffness can reduce building deformations. Flexural deformations are predominately induced by tunnel excavations beneath piles whereas horizontal strains at the ground level are negligible when a continuous foundation is included. Furthermore, it is illustrated that results based on buildings modelled as equivalent beams can differ considerably compared to when they are modelled as framed structures. Simple design charts are provided to estimate horizontal strains and deflection ratio modification factors based on newly defined relative axial and bending stiffness parameters which account for the presence of the piles.