The Elastic constants are calculated within vasp using IBRION=6 and ISIF=3. The Elastic constants are calculated from stress-strain relationship by applying finite distortion of lattice and ions. POTIM and NFREE are important parameter here.The elastic tensor is calculated both, for rigid ions, as well, as allowing for relaxation of the ions.
The elastic moduli for rigid ions are written after the line SYMMETRIZED ELASTIC MODULI (kBar).
The final elastic moduli including both, the contributions for distortions with rigid ions and the contributions from the ionic relaxations are written in TOTAL ELASTIC MODULI (kBar)
I am not a great fan of IBRION=6 which calculates elastic constants from stress-strain relationship. I prefer energy-stain relationship, where based on symmetry of crystal, we distort the crystal by several finite value followed by fitting the curve into second order polynomial to extract component of second order elastic constants. You can look into
vaspkit manual or any other package for performing calculation. It will cutdown computational cost by several fold.
Recently we have also developed a python based tool to calculate second order elastic constants from strain-energy method.