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<jats:p>Unusual quadratic dispersion of flexural vibrational mode and red-shift of Raman shift of in-plane mode with increasing layer-number are quite common and interesting in low-dimensional materials, but their physical origins still remain open questions. Combining <jats:italic>ab initio</jats:italic> density functional theory calculations with the empirical force-constant model, we study the lattice dynamics of two typical two-dimensional (2D) systems, few-layer h-BN and indium iodide (InI). We found that the unusual quadratic dispersion of flexural mode frequency on wave vector may be comprehended based on the competition between atomic interactions of different neighbors. Long-range interaction plays an essential role in determining the dynamic stability of the 2D systems. The frequency red-shift of in-plane Raman-active mode from monolayer to bulk arises mainly from the reduced long-range interaction due to the increasing screening effect.</jats:p>