Using the forced oscillation method and the ultrasonic transmission method, we measure the elastic moduli of a clay‐bearing Thüringen sandstone under dry and water‐saturated conditions in a broad frequency band at [0.004–10, 106] Hz for different differential pressures up to 30 MPa. Under water‐saturated condition, clear dispersion and attenuation for Young's modulus, Poisson's ratio, and Bulk modulus are observed at seismic frequencies, except for shear modulus. The measured dispersion and attenuation are mainly attributed to the drained/undrained transition, which considers the experimentally undrained boundary condition. Gassmann's predictions are consistent with the measured undrained bulk moduli but not with the shear moduli. Clear shear weakening is observed, and this water‐softening effect is stronger at seismic frequencies than at ultrasonic frequencies where stiffening effect related to squirt flow may mask real shear weakening. The reduction in surface free energy due to chemical interaction between pore fluid and rock frame, which is not taken into account by Gassmann's theory, is the main reason for the departure from Gassmann's predictions, especially for this rock containing a large number of clay minerals.