The study of the complex aerodynamics that characterise tiltrotors represents a challenge for computational fluid dynamics tools. URANS numerical solvers are typically used to explore the aerodynamic features that characterise the different flight conditions of these aircraft, but their computational cost limits their applications to a few vehicle configurations. The present work explores the capabilities of a new mid-fidelity aerodynamic code that is based on the vortex particle method, DUST, to investigate the performance and flow physics of tiltrotors. With this aim, numerical simulations were performed in DUST while considering XV-15 tiltrotor configurations with increasing complexity. The study started with the investigation of a simpler configuration made up of a single wing and a proprotor. Subsequently, the full aircraft was studied in steady-level flights and its major operating flight conditions were explored—i.e., hover, conversion phase, and cruise. A thorough assessment of the code capabilities was performed by the comparison of the numerical results with high-fidelity Computational Fluid Dynamics (CFD) data. This thorough comparison showed that the mid-fidelity numerical approach implemented in DUST is suitable for capturing the flow physics related to the complex aerodynamic interactions between the proprotors and the wing along with the entire flight envelope of the tiltrotor. Moreover, a good representation of the aerodynamic performance of the vehicle was obtained, particularly for the flight conditions that are characterised by limited flow separations. The good accuracy obtained for both the performance and flow physics, combined with the relatively lower computational costs required by the mid-fidelity solver with respect to the URANS simulations, indicates that DUST could be considered a valuable tool for use in the preliminary design of novel tiltrotor configurations.