Measurements of four of the five elastic stiffnesses of marine calcareous rocks and estimates of the fifth,c13, allow more detailed discussion of elastic wave propagation in these rocks than previously possible. The constantc13, which is seldom measured and was not measured in the rocks of this study, was derived by equating the Gassmann and Hashin‐Shtrikman estimates of the bulk moduli of chalk and limestone and then solving for the single unknownc13. For chalk, the measured constants, in N/m2×1010, arec11= 1.01,c33= 0.94,c44= 0.18, andc66= 0.21. For limestone, the measured constants, also in N/m2×1010, arec11= 2.41,c33= 2.09,c44= 0.47, andc66= 0.60. Three physically possible values ofc13were computed for chalk (0.48, 0.52, and 0.63 N/m2×1010) and for limestone (0.73, 1.05, and 1.24N /m2×1010). Heretofore, the only statements which could be made aboutc13in these rocks are |c13|<0.87×1010N/m2(chalk), and |c13|<1.94×1010N/m2(limestone). The calculations require the assumption that anisotropy in these rocks is caused by mineral alignment and the simplification of monomineralogy (calcite). On the basis of these measurements and estimates, the effect of elastic anisotropy on seismic reflection determinations of vertical compressional wave speed in calcareous rocks below the earth's surface is small ( ±6%), whereas similar determinations of vertically polarized shear wave speeds may be unreliable. Relationships are provided to convert seismic refraction measurements of horizontal compressional wave velocity to vertical velocity. These relationships are independent of the estimated valu