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Fully nonlinear numerical interaction of a transient wave with a three dimensional structure has been analysed based on a higher-order boundary element method (BEM). The BEM mesh on the free surface is generated through a combination of the structured and unstructured meshes. Through some auxiliary functions, the mutual dependence of fluid/structure motions is decoupled, which allows the body acceleration to be obtained without the knowledge of the pressure distribution. The solitary wave is used as the case study for the transient wave. It is obtained by the third order theory and the fully nonlinear theory. The accuracy of the present numerical model is verified through the steady propagation of a solitary wave and comparison with the published results for solitary wave interaction with a vertical wall. Simulations are then made to study solitary wave interaction with a truncated cylinder. Numerical results are provided for motions, forces and run-ups on the cylinder and comparison between results for the fixed cylinder and the freely floating cylinder is also made.