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Seismic wave propagation is affected by wave‐induced local fluid flow between stiff pores and multiscale fractures. To investigate this phenomenon, forced vibration (1–100 Hz) and ultrasonic (106 Hz) measurements are performed on two tight sandstones with complex pore geometry in dry and water‐saturated scenarios. Porosity, permeability, and ultrasonic velocities were also measured at different differential pressures. The results indicate that the nonlinear behavior of these properties is strongly influenced by the presence of cracks, and the correlations between the permeability/ultrasonic velocities and porosity are different. A wave propagation model is then developed in which penny‐shaped cracks are inclusions introduced stepwise into a porous medium to describe the wave anelasticity in a wide frequency band at different pressures. As a result, the model provides good agreement with the measured P‐wave velocity dispersion, and the pore aspect ratio spectrum and crack radii are determined. We then compare the estimated crack radii and pore size distributions from nuclear magnetic resonance spectroscopy. Published data of a tight sandstone and a low porosity sandstone in the frequency range (2–200, 106) and (1–3,000) Hz at different differential pressures are also analyzed to validate the model. The aspect ratios, volume fractions, and radii of pores/cracks are used to describe the measured permeability. The present work can provide new insights into the geophysical properties of reservoir rocks with complex pore geometry. Plain Language Summary: Multiscale cracks exert an important influence on the dispersion and attenuation of broadband acoustic waves. To better understand the underlying mechanism, we measured frequency‐dependent elastic moduli and pressure‐dependent porosity, permeability, and ultrasonic wave velocities of two tight sandstones. These data show that velocity dispersion is observable in water‐saturated rock and that permeability and ultrasonic velocities are differentially correlated with porosity. A proposed wave propagation model, in which penny‐shaped cracks are inclusions introduced stepwise into a porous medium, successfully describes the experimental data and other published data on tight sandstone and low‐porosity sandstone, and aspect ratios, volume fractions, and radii of pores/cracks are determined. Key Points: We propose a model to investigate the effect of multiscale cracks on seismic waves in tight sandstonesThe pore aspect ratio and crack‐radius spectra are estimated at different differential pressuresThe permeability is obtained according to the pore geometry [ABSTRACT FROM AUTHOR]