Abstract Lower and upper bounds of the peak horizontal ground acceleration are obtained through the consideration of the peak accelerations of two horizontal orthogonal components of the ground motion. Since the bounded region is relatively narrow, it is proposed to use the mean of the upper and lower bound accelerations as the peak horizontal ground acceleration. This mean value is equal to 1.20 times the larger peak acceleration of the two horizontal components of the ground motion. To support the proposed value, a simplified statistical analysis is also employed which results in a mean plus one standard deviation value for the peak horizontal ground acceleration of 1.24 times the larger peak acceleration. These conclusions are also supported by comparison with 50 pairs of earthquake acceleration records. For the resultant acceleration, the 50 pairs of records yield a mean plus one standard deviation estimate of the order of 1.20 times the larger peak acceleration.