Two principally different mechanisms of porosity reduction-induced elastic stiffening of siliciclastic rocks are recognized, which, in the domain of grain-supported siliciclastics with less than 15% volume clay, result in two linear trends with different slopes in the acoustic velocity-porosity plane. Transition between the two mechanisms occurs at about 30% porosity and roughly coincides with the transition from (1) early diagenesis, characterized by mechanical compaction and initial intergranular bonding, to (2) advanced chemical diagenesis caused by pressure solution and cementation. Peculiarities of velocity-stress relations in each of these diagenetic domains suggest that while the stress factor is important in loose sandstones, it has practically very little effect on the frame moduli of consolidated (less than about 30% porosity) sandstones at stress magnitudes beyond the closure stress of microcracks introduced by natural or coring-related processes. Appropriate grain contact and effective medium theories have been used to model the framework stiffening in the two diagenetic domains, respectively. It is shown that realistic, petrographically observed evolution of pore geometries in consolidated sandstones can be successfully modeled, resulting in a quasi-linear velocity-porosity relationship deviating from linearity within the accuracy of velocity measurements. A new look at the compilation of experimental data on acoustic velocities in clay matrix-supported siliciclastics (more than 15% volume clay), including 45 shales and 19 wackes, accounts for their distinct stress-sensitivity and anisotropy and suggests that their bedding-normal elastic stiffness varies nonlinearly in the whole range of porosity reduction from around 80% to almost zero. However, in the velocity-porosity plane below about 30% porosity, shales also show strong linear relationships with slopes subparallel to those of the grain-supported rocks.