Results of a parameter study on eccentric pounding of two symmetric single storey systems under seismic excitation are presented. Linear behaviour is assumed, and pounding effect is considered using the restitution coefficient approach. The effect of impact eccentricity is studied on two sets of symmetric models symmetrically and asymmetrically aligned with respect to each other for several gap widths, period dependent gaps and three values of the torsional-to-lateral frequency ratio. Two time histories are used for input. On the whole it was found that impact eccentricity amplifies the response relative to symmetric impact but the effect is not proportional to first impact eccentricity. Also, increasing gap width is likely to be effective when the separation is sufficiently wide practically to eliminate contact. Larger torsional rigidity tends to lower response amplification. SRSS code-type gaps appear to be adequate, or even excessive, when the design spectrum is compatible with the expected earthquake record at the site.