We numerically investigate the mode exciting properties of photoniccrystal fibres by using the beam propagation method when the optical fieldis input from a traditional single mode fibre. The results show thatboth the excited mode spectrum and the coupling-efficiency of eachexcited mode depend on the normalized pitch Ł/λ and thenormalized hole-size Ł/λ. Furthermore, we obtain the boundaryprofile of the optimizing coupling-efficiency for the excitedfundamental mode: the boundary (Ł/λ)* is linear to the boundary(d/Ł)*. All of these will pave the way for smoothingapplications of photonic-crystal fibres, such as splicing and designingphotonic-crystal-fibre functional devices.