The paper is concerned with finite element (FE) analysis of stress transfer from an elastic matrix to an elastic fibre, which need not be a uniform cylinder, in a fibre-reinforced composite material. Axisymmetric models of fibres embedded in co-axial cylindrical matrices were investigated by the FE method. Fibre shapes investigated were cylindrical, ellipsoidal, paraboloidal taper and conical taper. The effects of varying the fibre aspect ratio, q (ranging 200 to 3500) and Young's modulus (relative to that of the matrix), E-f/E-m (ranging 10(3) to 10(6)) were investigated. The results show that ellipsoidal and parabolic tapers lead to a similar distribution of interfacial shear stress (tau) to that observed for a uniform cylindrical fibre, except that the magnitude of the stress is higher. For a conical taper (except for q = 200, E-f/E-m = 10(6)), the interfacial stress increases to a maximum between the centre and the end of the fibre and then decreases towards the fibre ends. The effect of fibre taper on the distribution of tau values is reflected in the axial tensile stress, sigma(z), distribution induced in a fibre. For example, for a fibre with a conical taper, the distribution of tau values can lead to an even distribution of sigma(z) along the length of a fibre. (C) Koninklijke Brill NV, Leiden, 2010