This paper presents the R package HDclassif which is devoted to the clustering and the discriminant analysis of high-dimensional data. The classification methods proposed in the package result from a new parametrization of the Gaussian mixture model which combines the idea of dimension reduction and model constraints on the covariance matrices. The supervised classification method using this parametrization has been called High Dimensional Discriminant Analysis (HDDA). In a similar manner, the associated clustering method has been called High Dimensional Data Clustering (HDDC) and uses the Expectation-Maximization (EM) algorithm for inference. In order to correctly fit the data, both methods estimate the specific subspace and the intrinsic dimension of the groups. Due to the constraints on the covariance matrices, the number of parameters to estimate is significantly lower than other model-based methods and this allows the methods to be stable and efficient in high-dimensional spaces. Experiments on artificial and real datasets show that HDDC and HDDA perform better than existing classical methods on high-dimensional datasets, even with small datasets. HDclassif is a free software and distributed under the GNU General Public License, as part of the R software project.