This study investigates effect of uncertainty in natural vibration period on the seismic demand. It is shown that since this uncertainty affects the acceleration and displacement responses differently, two ratios, one relating peak acceleration responses and the other relating the peak displacement responses, are not equal and both must be employed in evaluating and defining the critical seismic demand. The evaluation of the ratios is carried out using more than 200 strong ground motion records. The results suggest that the uncertainty in the natural vibration period impacts significantly the statistics of the ratios relating the peak responses. By using the statistics of the ratios, a procedure and sets of empirical equations are developed for estimating the probability consistent seismic demand for both linear and nonlinear systems.