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Unusual quadratic dispersion of flexural vibrational mode and red-shift of Raman shift of in-plane mode with increas-ing layer-number are quite common and interesting in low-dimensional materials, but their physical origins still remain open questions. Combining ab initio 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 com-petition 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.