ESDU 04024 presents an introduction to rigid aeroplane response to gusts and atmospheric turbulence, together with the design criteria required to satisfy airworthiness requirements for both types of disturbance. The Item includes the vertical response of an aeroplane to a simple discrete sharp-edged gust, extension of this approach to accommodate the delays due to the build-up of lift and incidence and the further extension to a two degree-of-freedom model to provide lift and pitch response. Aeroplane response to atmospheric turbulence is provided through the relation between the frequency response function of an aeroplane and the methods of the power spectral density of a random variable. Appendix A presents a brief review of random variable theory introducing a description of the Fourier series and integral, introduction of the power-spectral density function and its relationship to the properties of stationary random processes including the mean, standard deviation and auto-correlation function. Appendix B introduces the relatively new statistical discrete gust method, which is a way to describe the more extreme gusts in a spectrum. This method, which does not form part of the airworthiness requirements, caters for gusts within the high frequency range of the spectrum, involves aeroplane responses in the time domain and uses sequences or families of discrete vertical gusts to formulate the probability of occurrence of a given sequence of gusts.