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Traditional binary-state systems have only two discrete system states: functional and non-functional. However, many practical facilities have more than two states and should be studied as a multi-state system (MSS). This chapter makes new contributions by modelling and analyzing the reliability and safety of MSSs with dependent component lifetimes. It discusses modelling and analyses of the reliability of dependent MSSs. The copula is used to model the dependent relationships of different components of an MSS. The copula connects a multivariate distribution to its marginal in such a way that it captures the entire dependence structure in the multivariate distribution. The copula selection problem can be split into three stages: get the lifetime data of components and the system; use a statistical method to estimate the parameters of the candidate copulas; and choose the appropriate copula from the candidates. The chapter presents a multi-state model, and the copula model is also applied to address the dependent relationship within the system.