The height of widespread tsunami runup about the Bay of Plenty from various volcanic scenarios involving eruptions at White Island is shown to be insignificant in all cases considered, except for Krakatoa‐type explosions. The problem of localised inundation remains unanswered. Some definitions describing volcanic tsunami risk, introduced recently by J. Latter(Bulletin volcanologique1982), are briefly mentioned. All numerical calculations assumed cylindrical symmetry and used a flux‐corrected Lax‐Wendroff algorithm to solve the modified shallow water equations of Peregrine.