The biomechanics of skin and underlying tissues plays a fundamental role in the human sense of touch. It governs the mechanics of contact between the skin and an object, the transmission of the mechanical signals through the skin, and their transduction into neural signals by the mechanoreceptors. To better understand the mechanics of touch, it is necessary to establish quantitative relationships between the loads imposed on the skin by an object, the state of stresses/strains at mechanoreceptor locations, and the resulting neural response. Towards this goal, 3-D finite-element models of human and monkey fingertips with realistic external geometries were developed. By computing fingertip model deformations under line loads, it was shown that a multi-layered model was necessary to match previously obtained in vivo data on skin surface displacements. An optimal ratio of elastic moduli of the layers was determined through numerical experiments whose results were matched with empirical data. Numerical values of the elastic moduli of the skin layers were obtained by matching computed results with empirically determined force-displacement relationships for a variety of indentors. Finally, as an example of the relevance of the model to the study of tactile neural response, the multilayered 3-D finite-element model was shown to be able to predict the responses of the slowly adapting type I (SA-I) mechanoreceptors to indentations by complex object shapes.