A new field formulation to replace the usual Gaussian approximation for weakly-guiding single mode fibres in some special applications is presented. It enables the field far from the core axis to be represented accurately in a simple form, but maintains the advantages of the Gaussian approximation method. This formulation can be useful in applications such as twin-core fibres and fibre couplers where the evanescent behaviour of the modal field outside the core region is of prime concern. Our method shows a significant improvement over the Gaussian method when applied to cases such as twin-core fibre couplers where large core separations are required for long coupling length devices.