The present article highlights the beneficial effect of considering soil and structure parameters uncertainties on the soil-structure response. The impedance functions of a circular foundation resting on a random soil layer over a homogeneous half-space were obtained by using cone models. The obtained results showed that the randomness of the layer's thickness and the shear wave velocity significantly affected the mean spring coefficients whereby coefficients of variation (COV) of 10% and 20% in these parameters reduced the mean spring coefficients about 32% and 40%, respectively, for the horizontal motion and about 12.5% and 25%, respectively, for the rocking motion. The sensitivity of the mean structural response to the randomness effect was obtained to be more pronounced to structural parameters than to soil parameters. In addition, 20% COV in both soil and structure parameters reduced the mean structural response about 39%, translated by an increase in the damping of the coupled system which may be considered as a beneficial effect from code provisions point of view.