The equations describing the elastic behavior of plane-wave disturbances in an infinite piezoelectric crystal are reduced in form to those of a purely elastic medium in the quasistatic approximation. The internal energy of the piezoelectric solid is expressed as one elastic-type term, and an alternative expression for the elastic energy flux yields the combined elastic and electric energy flux on replacing the elastic constant ${c}^{E}$ with the stiffened ${c}^{\mathrm{kD}}$ without introducing $\stackrel{\ensuremath{\rightarrow}}{\mathrm{\ensuremath{\nabla}}}\ifmmode\times\else\texttimes\fi{}\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}=\stackrel{\ensuremath{\rightarrow}}{\mathrm{D}}$ and $\stackrel{\ensuremath{\rightarrow}}{\mathrm{P}}=\stackrel{\ensuremath{\rightarrow}}{\mathrm{E}}\ifmmode\times\else\texttimes\fi{}\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}$. Similarly, the electric displacement is expressed in terms of the strain variables alone by means of modified piezoelectric ${e}^{\mathrm{kD}}$. Properties of this formalism and of the usual mechanical-electrical formulation are the same, and the two formulations are discussed in relation to each other. The elastic-propagation properties of piezoelectrics are describable by a ray or wave surface, which exists in terms of the ${c}^{\mathrm{kD}}$, and the techniques of variational elasticity carry over to piezoelectrics. The positive definiteness of the ${c}^{\mathrm{kD}}$ is asserted for an arbitrary direction to realize physical stability and, whereas no new limiting restrictions among material constants obtain, their use in Rayleigh-Ritz procedures assures its monotonic convergence. The symmetry and transformation properties of the ${c}^{\mathrm{kD}}$ show that, whereas their symmetry is lower than that of the ${c}^{E}$, their centrosymmetric nature requires only the centrosymmetric crystal groups to describe the elastic properties of piezoelectric crystals. Various stiffened-elastic properties are numerically evaluated for an arbitrary nonpure mode and symmetry-related directions for $\ensuremath{\alpha}$-quartz (class 32), LiNb${\mathrm{O}}_{3}$ ($3m$), CdS ($6mm$), ${\mathrm{Ba}}_{2}$Na${\mathrm{Nb}}_{5}$${\mathrm{O}}_{15}$ ($2mm$), ${\mathrm{Bi}}_{12}$Ge${\mathrm{O}}_{12}$ (23), and GaAs ($43m$). The work offers a simplified approach to characterizing bulk and surface elastic-wave properties of electroelastic waves in piezoelectric crystals and of modally analyzing particular classes of piezoelectric structures.