AbstractThe influence of insulating a structure with a soft first storey (horizontally elastic or elastoplastic or horizontally and vertically elastic) is investigated for horizontally propagating waves. A comprehensive parametric study for a simple structure excited by SH‐ and R‐waves is performed. A reactor building is examined for a horizontally propagating historic earthquake. Compared to a conventional structure, travelling‐wave effects become more important for R‐waves in a structure with a horizontal soft first storey. For SH‐waves, the opposit