Joint cylindrical distributions are key probability distributions that make possible a multivariate regression analysis as well as Markov models on a cylinder. In this study, some joint cylindrical distributions are proposed, and their statistical properties together with algorithms for random number generation are investigated. For proposed joint cylindrical distributions, the marginal distributions for various combinations of linear and circular variables are obtained. These marginal distributions are applied to the Markov process on a cylinder. The maximum likelihood estimation for unknown model parameters is investigated. To illustrate the applicability of the proposed models, time series analysis using wind speed and direction data is investigated.