In traditional earthquake-resistant design, peak ground acceleration (PGA) has been recognized as an important measure for evaluating earthquake- induced damages and assessing seismic risk of structures and ground deposits against natural hazards. However, it has become evident that PGA’s correlation with engineering demand parameters (EDPs) is relatively weak. As a result, this study first performs nonlinear dynamic analysis of shallow-founded buildings in liquefiable granular soils based on the effective stress analysis-based code, namely LIQCA3D. Sixty records of seismic motions are collected from the PEER NGA-West 2 database and chosen with various characteristics, such as moment magnitude (Mw), rupture distance (Rrup), Arias Intensity (IA), cumulative absolute velocity (CAV), and significant duration (Ds5-75). Secondly, this study explores the relationship between many well-established single and compound IMs and EDPs of shallow-founded buildings, i.e., buildings settlements and tilts. Finally, the study proposes the most appropriate IMs for effectively predicting EDPs and developing probabilistic seismic demand models (PSDMs) for shallow-founded buildings in liquefiable granular soils. The analytical findings reveal that cumulative absolute velocity (CAV) and sustained maximum velocity (SMV) are found to be the optimal single IMs, showing a high interrelation with settlement and tilt of buildings, respectively. However, recently developed compound IMs, such as CAV2/3 × Ds5-951/3 and SMV × Ds5-951/3, surpass the single IMs (i.e., CAV and SMV) in exhibiting the strongest correlation with earthquake-induced building settlement and tilts, accordingly.