Microbending plays a key role in the bend loss of optical fibres. To numerically investigate a microbending induced loss, an analytical model for microbending in optical fibres with arbitrary refractive index profiles is presented. In this model, random perturbations of the fibre core along the fibre axis are described by an analytical function whose power spectral density is derived from an exponential autocorrelation function. Using the model together with the beam propagation method, microbending loss is investigated for several different types of optical fibre, which include the traditional single-mode/multimode fibres (SMF/MMF) as used in existing optical networks, and typical few-mode/ring-core fibres (FMF/RCF) with the potential for future ultra high-speed optical networks. The validity of the proposed model is demonstrated by comparing the microbending loss of a SMF computed using coupled mode theory and the results. Simulation results show that, under the condition of launching only the fundamental mode into the optical fibres, the SMF and RCF supporting only one radial mode have nearly equal microbending loss, whilst the FMF and MMF have relatively low microbending loss. In addition, the microbending loss of the RCF is shown to be dependent on the ring core thickness.