Rupture directivity effects cause spatial variations in ground motion amplitude and duration around faults and cause differences between the strike-normal and strike-parallel components of horizontal ground motion amplitudes, which also have spatial variation around the fault. These variations become significant at a period of 0.6 second and generally grow in size with increasing period. We have developed modifications to empirical strong ground motion attenuation relations to account for the effects of rupture directivity on strong motion amplitudes and durations. The modifications are based on an empirical analysis of near-fault data. The ground motion parameters that are modified include the average horizontal response spectral acceleration, the duration of the acceleration time history, and the ratio of strike-normal to strike-parallel spectral acceleration. The parameters upon which the adjustments to average horizontal amplitude and duration depend are the fraction of the fault rupture that occurs on the part of the fault that lies between the hypocenter and the site, and the angle between the fault plane and the path from the hypocenter to the site. Since both of these parameters can be derived from the hypocenter location and the fault geometry, the model of rupture directivity effects on ground motions that we have developed can be directly included in probabilistic seismic hazard calculations. The spectral acceleration is larger for periods longer than 0.6 second, and the duration is smaller, when rupture propagates toward a site. For sites located close to faults, the strike-normal spectral acceleration is larger than the strike-parallel spectral acceleration at periods longer than 0.6 second in a manner that depends on magnitude, distance, and angle. To facilitate the selection of time histories that represent near-fault ground motion conditions in an appropriate manner, we provide a list of near-fault records indicating the rupture directivity parameters that each contains.