A comprehensive numerical model of a thulium-doped silica-based fibre amplifiers is presented. The model is spectrally and spatially resolved and is general in terms of pumping scheme used. The application of the model for predicting the S-band amplifier performance and for optimization of amplifier parameters is shown. For optimized Tm-doped fibre with 3 H4 level lifetime of 45 ls, which is the maximum value in the Tm-doped silica fibres prepared by the authors, above 20 dB of gain with 2000 mW pump power at the 1050 nm pump band can be expected according to the simulations.