In this study, analytical and numerical methods are used to examine the nonlinear dynamics of internal gravity waves forced by an isolated mountain and propagating upwards in a continously-stratified shear flow. An earlier numerical study (Campbell and Maslowe, 2003, JFM, 493) examined critical level interactions for a wave packet comprising a continuous spectrum of horizontal wavenumbers. Here we use analytical methods (multiple scaling and asymptotic methods) to study the specific case of an isolated mountain where the spectrum of horizontal wavenumbers is centred at zero. The problem is governed by two small parameters that define the height and width of the mountain and this allows us to carry out weakly-nonlinear analyses. We derive approximate solutions of the governing nonlinear time-dependent equations in order to study the interactions between the wave packet and the mean wind in the vicinity of the critical level. The analytical results are compared with the results of numerical simulations.