An approach to elastographic mapping in optical coherence tomography (OCT) using comparison of correlation stability of sequentially obtained intensity OCT images of the studied strained tissue is discussed. The basic idea is that for stiffer regions, the OCT image is distorted to a smaller degree. Consequently, cross-correlation maps obtained with compensation of trivial translational motion of the image parts using a sliding correlation window can represent the spatial distribution of the relative tissue stiffness. An important advantage of the proposed approach is that it allows one to avoid the stage of local-strain reconstruction via error-sensitive numerical differentiation of experimentally determined displacements. Another advantage is that the correlation stability (CS) approach intrinsically implies that for deformed softer tissue regions, cross-correlation should already be strongly decreased in contrast to the approaches based on initial reconstruction of displacements. This feature determines a much wider strain range of operability than the proposed approach and is favorable for its free-hand implementation using the OCT probe itself to deform the tissue. The CS approach can be implemented using either the image elements reflecting morphological structure of the tissue or performing the speckle-level cross-correlation. Examples of numerical simulations and experimental demonstrations using both phantom samples and in vivo obtained OCT images are presented.