We describe the use of elastographic processing in phase-sensitive optical coherence tomography (OCT) for visualizing dynamics of strain and tissue-shape changes during laser-induced photothermal corneal reshaping, for applications in the emerging field of non-destructive and non-ablative (non-LASIK) laser vision correction. The proposed phase-processing approach based on fairly sparse data acquisition enabled rapid data processing and near-real-time visualization of dynamic strains. The approach avoids conventional phase unwrapping, yet allows for mapping strains even for significantly supra-wavelength inter-frame displacements of scatterers accompanied by multiple phase-wrapping. These developments bode well for real-time feedback systems for controlling the dynamics of corneal deformation with 10-100 ms temporal resolution, and for suitably long-term monitoring of resultant reshaping of the cornea. In ex-vivo experiments with excised rabbit eyes, we demonstrate temporal plastification of cornea that allows shape changes relevant for vision-correction applications without affecting its transparency. We demonstrate OCT's ability to detect achieving of threshold temperatures required for tissue plastification and simultaneously characterize transient and cumulative strain distributions, surface displacements, and scattering tissue properties. Comparison with previously used methods for studying laser-induced reshaping of cartilaginous tissues and numerical simulations is performed.