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This paper presents an approximate analytical solution for the vertical dynamic impedance and shaft resistance of rectangular closed diaphragm walls (RCDWs) embedded in a homogeneous soil medium and resting on rock base. The vertical continuous displacement model for the steady-state response of RCDWs is proposed to ensure proper RCDWs-soil contact and satisfy the boundary condition of soil at infinite horizontal distance. The soil horizontal displacement is neglected and the effect is indirectly taken into account by the modification of soil modulus. The functional of system potential and kinetic energies is established via the soil and RCDWs displacement functions. The governing equations of the system and the relevant conditions are obtained and the vertical shaft resistance of RCDWs is established by employing Hamilton's variational principle for RCDWs-soil system and thin layer element, respectively. Some representative numerical examples are presented to portray the influences of soil core ratio, height–width ratio, diaphragm wall-soil stiffness ratio, and aspect ratio of RCDWs cross sections on the dynamic impedances and stiffness of the shaft resistance. [ABSTRACT FROM AUTHOR]