A detailed variational analysis of single-mode trapezoidal index fibre to investigate its propagation characteristics involving two simple approximations of fundamental mode is presented. It is shown in respect of computation of normalized field that the single parameter variational function having Gaussian and modified Bessel variations in the core and cladding, respectively, is more accurate in comparison with the Gaussian function over a wide range of values of normalized frequency and aspect ratio. Also, it predicts the propagation characteristics, more accurately, than the Gaussian function from variational and recently reported Marcuse-type formulations. Further, in terms of such range of values, a complete formulation of variational parameter for the Gaussian-modified Bessel function is prescribed for ready reference to the system users to predict the modal field and propagation characteristics. © 2016 Informa UK Limited, trading as Taylor & Francis Group.