Local lattice displacements in the copper oxide superconductors are determined by polarized Cu K‐edge extended x‐ray absorption fine structure (EXAFS) measurements. Temperature dependent local atomic displacements show anomalies, at the Tcand a temperature Tswhere the charge inhomogeneous state appears, as revealed by a change in the correlated Debye‐Waller factor (DWF) of the Cu&sngbnd;O bonds. While the DWF shows a clear drop at the Tc, an order parameter like up‐turn appears at the Ts. The anomalies shows‐up with different amplitude, depending on the superconducting transition temperature of the system and the micro‐strain in the electronically active CuO2plane. The measured Cu&sngbnd;O displacements appear to be closely related to the kink structure in the angle resolved photoemission experiments. The results are discussed to find some correlation between electron‐lattice coupling, inhomogeneous charge state and superconductivity in the copper oxides. © 2003 American Institute of Physics