This study developed a model for predicting the response, in terms of amplitude versus frequency of single piles under lateral vibratory loadings embedded in clay or fine silty soils. The model incorporates frequency dependent parameters and the effects of soil non-linearity through the relationship between soil shear modulus and damping with strain. A computer program, Dyna5, was used to generate the computed response of single piles using the Novak and El-Sharnouby (1983) approach. Soil non-linearity was accounted for by incorporating spline interpolation routine into Dyna5. Sliding and coupled rocking vibrations were addressed. The computed responses were predicted and compared with the measured data in terms of resonant amplitudes and resonant frequencies. The computed responses show higher natural frequencies and lower resonant amplitudes than those determined from field tests. That difference is mainly due to overestimated soil shear modulus and damping used in the computations. Empirical equations relating the reduction factors with soil and pile properties are proposed and validated using different sets of experimental tests.