We report on the method of TiO2 nano- and microfibres preparation and their cracking during processing and post-treatment. Nano- and microfibres were fabricated by drawing from viscous alkoxide based oligomeric concentrate precursors with the following exposure into an atmosphere of 30-50% humidity. The fibres microstructure was analyzed with TEM, solid state NMR, X-ray diffraction tools, and AFM. Experiments on crack formation in TiO2 microfibres proved that fibres with diameter larger than 10 micron are fractured for chosen post-treatment regimes. In theoretical considerations sol-gel produced and thermally treated microfibres are modeled as core/shell structures. It is suggested that the formation of fibres starts via solidification of liquid jet through the appearance of a rigid solid shell, which reveals tensile mechanical stresses because of material shrinkage. The effect of post-treatment is taken into account by additional densification of the fibre surface layer. The stress intensity factor K(I) is calculated for the model core/shell structures and the dependence of K(I) on the fibre diameter is demonstrated. The results of modeling qualitatively confirm experimental data of microfibre cracking above a certain threshold diameter.