AbstractThe purpose of the paper is to study the applicability of stochastic methods for determining the response in the vertical plane of long‐span bridges to earthquakes. The bridges are of the modern type, with flexible towers, box‐decks and inclined hangers, Humber and Bosporus being used as the main examples, although some useful information is obtained by studying a small suspension footbridge. The input ground acceleration is that of the Pacoima Dam record of the 1971 San Fernando event, but use is also made of filtered white noise.Because the stochastic approach is essentially an attempt to abstract usable information which could otherwise be obtained from a lengthy time‐history approach, the procedure adopted here is to compare the same parameters obtained in these two ways, as far as possible. In particular, the maximum values of displacements and bending moments are considered.The essential question to be answered is whether the short length of earthquake records, coupled with the large natural periods of vibration of long‐span bridges, allows sufficient response information to be generated to make statistical parameters meaningful. The short‐span (50 m) footbridge gives no cause for concern here, but the detailed comparison with time‐history solutions shows that the stochastic approach for both Bosporus and Humber has to be cautiously assessed, particularly if some trailing zeros are not added to the earthquake record. However, general conclusions are not made, because only one earthquake record ha