The class of CUB models is commonly used by practitioners to model ordinal data, in this paper we propose the cubm package which provides the class of CUB models in the R system for statistical computing. The cubm package allows to specify a formula for each parameter of the model, the Maximum Likelihood (ML) estimation is performed by optimization via the functions nlminb, optim and DEoptim and the variance-covariance matrix can be obtained by numerical approximation of the Hessian matrix or by bootstrap method. The utility of the package is illustrated by an application and a simulation study.