Wind pressure fluctuations acting on low building roofs are important for the prediction of peak pressure values and for fatigue design purposes. Collection of several time histories of pressure fluctuations, using traditional wind tunnel measurements is time consuming and expensive. Within this context, a systematic study on the development of an efficient and practical method of digitally simulating realizations of local wind pressure time series has been carried out.  The stochastic characteristics of wind pressure fluctuations acting on various low building roofs have been investigated by using systematic wind tunnel measurements. Thereafter, based on the Fourier representation of time series, a new time series generation technique capable of simulating Gaussian as well as non-Gaussian wind pressure fluctuations is developed. Both Fourier amplitude and phase, which are required for the simulations, are modelled individually. The Fourier amplitude part is constructed either from sample time history or from sample spectra, while a simple stochastic model is proposed for the generation of Fourier phase of non-Gaussian time series. In the present study, the criterion for successful modelling is set to preserve the first four moments (mean, variance, skewness and kurtosis) and spectra of the corresponding pressure fluctuations. The efficiency of this novel methodology is illustrated with several examples.  Several measured wind pressure spectra have been investigated to determine characteristic spectral shapes and derive a suitable mathematical representation. Based on the similarities among normalized spectra, an empirical model has been suggested for the synthetic generation of normalized spectra. Such artificially produced pressure spectra have been utilized for the generation of Fourier amplitude part in subsequent simulations. Thereafter, for easy generation of pressure time histories on roofs, normalized spectra are categorized for each roof and the standard spectral shapes associated with various zones of each roof and their parameters are established.  Further, potential applications of the proposed simulation methodology in extreme value as well as fatigue analysis are presented. In particular, the fatigue analysis of roof cladding using simulated pressure fluctuations has been described in detail