The scalar propagation characteristics of a bent optical waveguide are investigated. Using a first-order perturbation theory, analytic solutions for the fields and propagation constants of any mode, of either even or odd symmetry, are obtained. The bend breaks the degeneracy of the higher-order scalar propagation constants, and the modes become truly polarised with fixed field directions in the fibre. A more exact analysis is used to investigate the modal properties of the bent slab waveguide, and an expression for the radiation point, which is the point in the cladding at which the field becomes radiative, is derived. Using a Gaussian function to approximate the fields, the range of validity of the perturbation expansion is discussed.