SummaryThe response of a rigid block supported on a horizontally moving foundation through a dry‐friction contact is investigated to near‐fault ground motions. Such motions can be thought of as consisting of a coherent component (‘pulse’) and an incoherent component, which can be described as a band‐limited ‘random noise’. The equation of motion of this strongly nonlinear system is reduced to a normalized form that reveals important parameters of the problem such as the critical acceleration ratio. The response of the sliding block to a set of uniformly processed near‐fault motions, covering a sufficiently wide range of magnitudes, is evaluated numerically for selected discrete values of the acceleration ratio. For each value of the critical acceleration ratio, the numerically computed residual slips are fitted with a Weibull (Gumbel type III) extreme value probability distribution. This allows the establishment of regression equations that describe accurately design sliding curves corresponding to various levels of non‐exceedance probability. The analysis reveals that the coherent component of motion contributes significantly to the response of the sliding block. Furthermore, the relevant acceleration in specifying the critical acceleration ratio is the (normalized) amplitude, αH_pulse, of the pulse and not the (normalized) amplitude of the incoherent component αH. Finally, the incoherent component is described quantitatively in terms of the root‐mean‐square acceleration aRMS, and an attempt is made to understand its influence on the response of the sliding block. Copyright © 2016 John Wiley & Sons, Ltd.