Under-deck cable-stayed bridges are very efficient structures that allow for slender and light-weight designs. Renowned engineers and researchers worldwide have paid a significant attention to these structures in recent years. Unlike conventional highway bridges with concrete girders, the users comfort typically governs the design of the deck in under-deck cable-stayed bridges in order to prevent excessive vibrations from the traffic live load. In this research work an innovative vehicle-bridge interaction model is employed to consider the influence of the vehicle wheel dimensions on the serviceability state of vibrations. The vehicle-bridge interaction model also includes the flexibility and damping of the tyre and suspension systems, capturing accurately the yaw, roll and pitching motions of the truck body. Rigorous nonlinear dynamic analyses are conducted in ABAQUS by using fully three dimensional finite element models of several under-deck cable-stayed bridges. These structures span a distance of 80 metres with a depth-to-span ratio of 1/80. Four different road categories, three wheel radii and two types of bridge articulation have been considered. The importance of the road roughness combined with the wheel dimensions of heavy trucks has been clearly observed from the numerical results. Different criteria provided by normative and previous research works have been employed and discussed to assess the comfort of pedestrians and vehicle users.