Stochastic seismic response analysis and reliability evaluation of base-isolated structures are conducted combining the physical stochastic ground motion model and the probability density evolution method. Three cases are investigated, including the base-isolated structure subjected to frequent earthquake of intensity 8, the identical super structure with fixed base subjected to frequent earthquake of intensity 7, and the base-isolated structure subjected to rare earthquake of intensity 8. Comparative studies reveal and verify some features of performances of base-isolated structures from the point of view of random vibration. The base-isolated super structure behaves like a near rigid body when subjected to small earthquakes while under strong earthquakes the first mode shape dominates the responses with ignorable effects of higher-order mode shapes. The response and earthquake action on the super structure could be reduced by one degree of intensity. Dynamic reliabilities against different response indices of the structure in different cases are evaluated. The investigations show that stochastic seismic response analysis and reliability assessment could provide indices for decision making more objective than just a few selected deterministic ground motions as usually employed in practice.