The problem of face identification is considered as that of featureless similarity-based pattern recognition. In terms of the support object approach, we use a kernel function of two gray-level vectors for measuring the pair-wise proximity of face images. In addition to the usual kind of kernel functions called here rigid because of their being formed by way of immediate comparison of two gray-level distributions on the original image plane, we examine a new class of kernel functions which we call elastic ones. The principal idea of elastic kernel functions consists in an elastic transformation of the pixel grid of one image relative to that of the other, so that the positions of all identical elements in both faces would become the same.