Objectives  As a high-tech ship, the trimaran is particularly prominent in structural strength. Traditional numerical methods are analysed by deterministic methods. However, such variables as the loads acting on the hull, the uncertainty of the calculating model and the performance of the material are random. Therefore, reliability measures are taken to account for the influence of these factors on hull strength.

  Methods  The three-dimensional potential flow theory and direct calculation of strength for the hull structure are used in this paper to obtain the short-term time-period distribution of the von Mises stress of special structural elements, then the distributions of long-term von Mises stress and sequence statistics of extreme value are obtained. The limit state equation is listed in combination with the structural capacity and load requirements of the units to obtain the reliability indexes. The failure probability and safety factor of typical structures are calculated, and certain random components are analysed on impact.

  Results  The research shows that the structural strength of a trimaran is concentrated at the connecting bridge, the safety factor is 0.86 and the deck safety factor is 2.4. Due to the high neutral axis, the material uncertainty has a greater influence on the reliability indexes.

  Conclusions  The method of yield strength reliability research for trimaran proposed in the study can provide good data-support for the optimization of trimarans.