The paper presents a method for the analysis of generalised wire antennas and scatterers, consisting of right truncated cones of circular cross-section interconnected in an arbitrary manner. The integral equation for current distribution is derived starting from the local and extended boundary conditions for the electric field, enabling the efficient analysis of both hollow and solid cones. An entire domain current expansion for a series connection of n ≥ 1 truncated cones is proposed, that enables curved wires to be approximated by any number of straight segments without increasing the number of unknown coefficients. A method for obtaining the expansions starting from arbitrary function sets which satisfy the continuity equation at the segment interconnections and ends is also presented. With such basis functions, the solution of the integral equations by means of the Galerkin method is shown to require(a) A remarkably small number of unknowns per wavelength (e.g. two with the combined polynomial/trigonometric current expansion)(b) A remarkably short time of evaluation of the impedance matrix.The results obtained by the method are in good agreement with available experimental and numerical results.