We have investigated the local structure of BiS2-based layered materials by Bi L3-edge extended X-ray absorption fine structure (EXAFS) measurements performed on single crystal samples with polarization of the X-ray beam parallel to the BiS2 plane. The results confirm highly instable nature of BiS2 layer, characterized by ferroelectric like distortions. The distortion amplitude, determined by the separation between the two in-plane (Bi-S1) bonds, is found to be highest in LaO0.77F0.23BiS2 with ΔR∼0.26 Å and lowest in NdO0.71F0.29BiS2 with ΔR∼0.13 Å. Among the systems with intrinsic doping, CeOBiS2 shows smaller distortion (ΔR∼0.15 Å) than PrOBiS2 (ΔR∼0.18 Å) while the highest distortion appears for EuFBiS2 revealing ΔR∼0.22 Å. It appears that the distortion amplitude is controlled by the nature of the RE(O,F) spacer layer in the RE(O,F)BiS2 structure. The X-ray absorption near edge structure (XANES) spectra, probing the local geometry, shows a spectral weight transfer that evolves systematically with the distortion amplitude in the BiS2-layer. The results provide a quantitative measurements of the local distortions in the instable BiS2-layer with direct implication on the physical properties of these materials.