Summary. In mixture experiments, one may be interested in estimating not only main effects but also some interactions. Main effects and significant interactions in a mixture may be estimated through appropriate mixture experiments, such as simplex‐centroid designs. However, for mixtures with a large number of factors, the run size for these designs becomes impractically large. A subset of a full simplex‐centroid design may be used, but the problem remains regarding which factor‐level settings should be selected. In this paper, we propose a solution that considers design points with either one or p individual nonzero factor‐level settings. These fractional simplex designs provide a means of screening for interactions and of investigating the behavior of many‐component mixtures as a whole while greatly reducing the run size compared with full simplex‐centroid designs. The means of construction of the design arrays is described, and designs for ≤31 factors are presented. Some of the proposed methodology is illustrated using generated data.