This paper presents a study of acceleration demands in low-rise reinforced concrete (RC) buildings with torsion, evaluated by quantifying peak floor accelerations (PFAs) and floor response (acceleration) spectra (FRS). The study was performed with the aim to provide simple empirical formulas to quantify the amplification effects due to torsion, which can occur in most of the existing and new RC buildings. With this goal in mind, a set of eight archetype buildings was selected, characterized by an increasing floor eccentricity obtained by moving the centre of rigidity (CR) away from the centre of mass (CM). Numerical models of the proposed set of archetype RC buildings were considered in both linear elastic and nonlinear configurations. For the latter, the properties of models were widely varied, by systematically modifying parameters of plastic hinges, in order to obtain a sample of 1000 models. Non-structural components (NSCs) were considered linear elastic in all cases. To investigate acceleration demands, a set of forty Eurocode 8 spectrum-compatible ground motion records were used as input. For linear elastic building models, it was observed that the change of demands depends on the position of the NSC (in-plan and in-height), and on the distance between CR and CM. On the other hand, for nonlinear models, additional parameters must be considered, such as the building ductility (μ) and yielding force (Vy). New regression models were proposed for quantifying the observed differences in PFAs and FRS when torsion occurs. The efficiency of the proposed models was assessed by testing the new formulas on an existing case study building, as well as on the well-known SPEAR building.