We evaluated a viscoelastic modeling of P- and S-wave velocity dispersion, attenuation, pressure, and fluid effects for a set of siliciclastic rock samples. Our analysis used a published laboratory data set of 63 sandstones with a wide range of compositional heterogeneities. We observed a notable correlation between the (velocity and attenuation) pressure sensitivity and the abundance/lack of quartz in the samples. We included compliant pores (low-aspect ratio) proportionally to the content of secondary minerals to account for the differential sensitivity to pressure. The observed velocity and attenuation were well reproduced by the applied viscoelastic modeling. We found that pores of significantly different scale required pore fluid relaxation time constants of proportionally different magnitudes to reproduce the velocity and attenuation measurements. The relaxation time constant of crack-sized pores can be one order of magnitude smaller than the constant of mesopores. Moreover, the velocity dispersion and attenuation signatures revealed that a pore textural model dependent on lithological composition is critical in the prediction of time-lapse fluid and pressure responses.