A method for the dynamic response analysis of horizontally layered soils in terms of effective stresses is developed and used to study the effects of a number of parameters on the response characteristics of a soil deposit. The deposit is represented as a series of lumped masses connected with shear springs, and is subjected to vertically propagating shear waves. The shape of the stress-strain relationship in soils under cyclic loading conditions reflects the soil nonlinearity and the mechanism of energy loss. A review of soil modelling is made, and it is found that the hyperbolic stress-strain model with load reversal combines simplicity, easy computer manipulation and the desired degree of accuracy for the range of engineering problems. A modification of the model for a better approximation of experimental results is introduced and used in the subsequent nonlinear analysis. The response of the pore water pressure during cyclic loading of fully saturated soils is also studied, and a new model for estimating the excess pore water pressure increase is proposed. The stress-strain and the pore pressure models are coupled and used in a dynamic response analysis in terms of effective stresses. There are many methods available to integrate directly the equations of motion of lumped parameters structural systems. The linear operators associated with some of these methods for computing the response of undamped simple oscillators are studied with regard to stability and accuracy. A method based on a parabolic variation of the acceleration is used in the present research. The analyses reveal substantial differences between the response computed in terms of effective stresses and that in terms of total stresses, the latter overestimating the liquefaction potential of the deposit as well as the induced accelerations and underestimating the induced displacements. There is also a considerable effect of the bedrock motion intensity on the response characteristics of the deposit, and under certain conditions a weak motion can induce larger accelerations than a stronger motion. The results also show that large ground accelerations can be transmitted to a structure only through strong soil deposits. Weak foundation materials act as a cut-off to the transmission of large accelerations at the expense of large displacements. Finally, the presence of a mass on the surface of the deposit results in the transmission of larger accelerations than the normal case.