It is reported that supercontinuum spectrum from 440 to 1050 nm can be generated in holey microstructure fibres (HMFs) with random cladding distribution by Ti:sapphire femtosecond laser pulses with central wavelength of 800 nm. Based on the method of the effective refractive index and the analogy of step-index fibre, we have calculated the effective mode area and the group velocity dispersion (GVD). It is found that the HMFs have specifically ability of localizing light and controlling GVD. The mechanism of supercontinuum generation in the HMFs with random cladding distribution is that the balance between the GVD and the self-phase modulation in the anomalous dispersion region leads to formation of solitons and fission of high order solitons.