Tactile performance of human fingertips is associated with activity of the nerve endings and sensitivity of the soft tissue within the fingertip to the static and dynamic skin indentation. The nerve endings in the fingertips sense the stress/strain states developed within the soft tissue, which are affected by the material properties of the tissues. The vibrotactile sensation and tactile performance are thus believed to be strongly influenced by the nonlinear and time-dependent properties of the soft tissues. The purpose of the present research is to simulate the biomechanics of tactile sensation. A two-dimensional model, which incorporates the essential anatomical structures of a finger (i.e. skin, subcutaneous tissue, bone, and nail), has been used for the analysis. The skin tissue is assumed to be hyperelastic and viscoelastic. The subcutaneous tissue is considered to be a nonlinear, biphasic material composed of a hyperelastic solid and an inviscid fluid phase. The nail and bone are considered to be linearly elastic. The advantages of the proposed fingertip model over the previous "waterbed" and "continuum" fingertip models include its ability to predict the deflection profile of the fingertip surface, the stress and strain distributions within the soft tissue, and most importantly, the dynamic response of the fingertip to mechanical stimuli. The proposed model is applied to simulate the mechanical responses of a fingertip under a line load, and in one-point (1PT) and two-point (2PT) tactile discrimination tests. The model's predictions of the deflection profiles of a fingertip surface under a line load agree well with the reported experimental data. Assuming that the mechanoreceptors in the dermis sense the stimuli associated with normal strains (the vertical and horizontal strains) and strain energy density, our numerical results suggest that the threshold of 2PT discrimination may lie between 2.0 and 3.0 mm, which is consistent with the published experimental data. The present study represents an effort to develop a structural model of the fingertip that incorporates its anatomical structure, and the nonlinear and time-dependent properties of the soft tissues.