As an important class of space-filling designs, uniform designs (UDs) choose a set of points over a certain domain such that these points are uniformly scattered, under a specific discrepancy measure. They have been applied successfully in many industrial and scientific experiments since they appeared in 1980. A noteworthy and practical advantage is their ability to investigate a large number of high-level factors simultaneously with a fairly economical set of experimental runs. As a result, UDs can be properly used as experimental plans that are intended to derive the significant factors from a list of many potential ones. To this end, a new screening procedure is introduced via penalized least squares. A simulation study is conducted to support the proposed method, which reveals that it can be considered quite promising and expedient, as judged in terms of Type I and Type II error rates.