We have provided new insights into the controlling factors of elastic properties in continental carbonate rocks and introduced an applicable model for acoustic-velocity predictions in such a medium. Petrophysical properties (porosity, permeability, P- and S-wave velocities) from laboratory measurements have been coupled with thin-section observations and characterizations, and X-ray diffraction (XRD) analyses. A major achievement is the establishment of the link between the mineralogical composition and the P- and S-wave velocity dispersion at a given porosity. This reflects the subtle interplay between physicochemical and biological precipitation of continental carbonates, which can also be associated with a strong influence of detrital mineralogical inputs. The result is a mineralogical commixture, coupled to a wide array of pore types inherited from the strong ability of carbonate rocks to undergo diagenetic alteration. The proposed model takes into account the elastic moduli of the minerals, porosity, and pore shape, and it is based on the effective medium theory. We have considered the case in which the medium contained randomly oriented pores with different aspect ratios. Overall, the fit between the predicted trends and the experimental data is fairly good, especially for calcite and quartz matrix mineralogy. The results are even better when considering mineralogy inferred from XRD data, although in some case, and despite the aspect ratio variation in both simulations, the model fails to accurately predict the P-wave velocities. This probably means that another factor is at stake beside mineralogy. This can be explained by the limitation of the effective medium approach, which oversimplifies the reality and fails to account for the variability of some aspect ratio from one inclusion to another.