<p>Multi-site stochastic models consist of a rich class of models that can be utilised to analyse environmental data and provide a range of possible inputs to hydrological models to quantify uncertainty and assess risk in environmental systems. We develop a class of multi-site hidden Markov models that incorporate a copula to capture the characteristics of the daily precipitation process across a network of stations. The construction of the likelihood function of the proposed multi-site precipitation models is described. A copula with appropriate dependence structure is selected from the family of Archimedean copulas. The maximum likelihood method is used to estimate the parameters of the models. The proposed class of models is used to analyse twelve years of daily rainfall data from four weather stations in London, England. The copula-embedded multi-site models captured the properties of the daily rainfall well and reproduced the correlation structure of the daily precipitation better than the other hidden Markov models.</p>