The performance of the Q-switched erbium-doped fibre laser with two fibre Bragg gratings as cavity mirrors was theoretically analysed, employing a set of rate equations for the ion populations and the photon flux inside the cavity. The simulation considers a system where the pulsed laser emission is produced by the temporal modulation of a Bragg grating fixed to a piezoelectric and operating in the 1550 nm spectral region. The temporal evolution of different frequency components of the laser emission produced is governed by the instantaneous overlap between the two gratings. Theoretical results are in agreement with previously reported experimental values.