Ultrasonic vibration is employed to modify the friction of a finger pad in way that induces haptic sensations. A combination of intermittent contact and squeeze film levitation has been previously proposed as the most probable mechanism. In this paper, in order to understand the underlying principles that govern friction modulation by intermittent contact, numerical models based on finite element (FE) analysis and also a spring-Coulombic slider are developed. The physical input parameters for the FE model are optimised by measuring the contact phase shift between a finger pad and a vibrating plate. The spring-slider model assists in the interpretation of the FE model and leads to the identification of a dimensionless group that allows the calculated coefficient of friction to be approximately superimposed onto an exponential function of the dimensionless group. Thus, it is possible to rationalise the computed relative reduction in friction being (i) dependent on the vibrational amplitude, frequency, and the intrinsic coefficient of friction of the device, and the reciprocal of the exploration velocity, and (ii) independent of the applied normal force, and the shear and extensional elastic moduli of the finger skin provided that intermittent contact is sufficiently well developed. Experimental validation of the modelling using real and artificial fingertips will be reported in part 2 of this work, which supports the current modelling.