Motivated by a laboratory experiment reported in Alben, Shelley & Zhang (Nature, vol. 420, 2002, p. 479), we performed simulations of an elastic fibre anchored at its centre point and immersed in a flowing viscous incompressible fluid by the immersed boundary (IB) method. We focus on the influence of some dimensionless parameters on vortex shedding from the fibre for Re in the range [30, 800]. Three sets of simulationswere designed to investigate the influence of Reynolds number Re, dimensionless fibre flexure modulus b, and dimensionless fibre length on vortex shedding. According to the simulation results, Re, b, and each has a significant influence on the structure of shed vortices. However, Re has little influence on the vortex shedding frequency. With the increase of dimensionless bending modulus, the dimensionless vortex shedding frequency (fvs) and the critical Reynolds number (Rec) decrease approximately as power-law functions. Both fvs and Rec increase approximately linearly as dimensionless fibre length increases.