Gene set analysis (GSA) aims to evaluate the association between the expression of biological pathways, or a priori defined gene sets, and a particular phenotype. Numerous GSA methods have been proposed to assess the enrichment of sets of genes. However, most methods are developed with respect to a specific alternative scenario, such as a differential mean pattern or a differential coexpression. Moreover, a very limited number of methods can handle either binary, categorical, or continuous phenotypes. In this paper, we develop two novel GSA tests, called SDRs, based on the sufficient dimension reduction technique, which aims to capture sufficient information about the relationship between genes and the phenotype. The advantages of our proposed methods are that they allow for categorical and continuous phenotypes, and they are also able to identify a variety of enriched gene sets.