Conventional steel-concrete composite floors comprising of steel sections and sheeting, cast in situ concrete and embedded stud shear connectors are made from energy- and carbon-intensive construction materials, viz. concrete and steel. Replacing conventional reinforced concrete floors with solid timber, in particular cross-laminated timber (CLT) with improved stability and structural characteristics, can significantly increase the speed of construction, reduce the need for rigging and craneage and also lower the self-weight of the building, the size of the columns and foundations and therefore the overall carbon footprint of the building. However, experimental data on the short- and long-term structural performance of steel-timber composite (STC) floors under service loading conditions are scarce and no long-term theoretical analyses of steel-timber composite floors have been reported hitherto in the literature. Accordingly, non-linear 1-D frame finite element models are developed in this paper, and validated against experimental data on timber and hybrid timber composite beams. The numerical tool is then employed to predict the long-term stiffness and load-deflection response of STC floors under service loading conditions. A parametric study is carried out and the influence of the stiffness of the shear connectors, timber shrinkage, creep, hydro-expansion and mechano-sorptive effect on the long-term behaviour of the STC beams are investigated.