Aims.We discuss a simple model of a line-tied coronal arcade with piecewise constant density to explore the effects of curvature on radially polarised fast modes.Methods.A partial differential equation is derived for the velocity perturbation of the fast modes and it is solved analytically in terms of Bessel functions of half integer order, obtaining a dispersion relation.Results.The properties of the modes are studied in terms of the parameters. All the modes are leaky under these conditions. Besides the usual kink and sausage modes, new families are described: the vertical, swaying (longitudinal), and rocking modes arise.Conclusions.The damping rates are similar to observed rates. For thin arcades the modes are markedly different from those of a straight slab and resemble more the modes of a circular membrane.