Clifftop coastal boulders transported by storm waves or tsunamis have been reported around the world. Although numerical calculation of boulder transport is a strong tool for the identification of tsunami or storm boulders, and for estimation of the wave size emplacing boulders, models which can reasonably solve boulder transport from below a cliff or from a cliff‐edge onto a cliff‐top do not yet exist. In this study, we developed a new numerical formulation for cliff‐top deposition of boulders from the cliff edge or below the cliff, with validation from laboratory tests. We then applied the model using storm and tsunami wave forcing to simulate the observed boulder deposits at the northwest coast of Hachijo Island, Japan. Using the model, the actual distribution of boulders was explained well using a reasonable storm wave height without assumption of anomalously high‐water level by storm surge. Results show that boulder transport from the cliff edge or under the cliff onto the cliff‐top was possible from a tsunami with periods of 5~10 min or storm waves with no storm surge. However, the actual distribution of boulders on the cliff was explained only by storm waves, but not by tsunami. Therefore, the boulders distributed at this site are likely of storm wave origin. Our developed model for the boulder transport calculation can be useful for identifying a boulder's origin and can reasonably calculate cliff‐top deposition of boulders by tsunami and storm waves. © 2019 John Wiley & Sons, Ltd. © 2019 John Wiley & Sons, Ltd.