Expansin is a type of cell wall elongation and stress relaxation protein involved in various developmental processes and stress resistances in plant. In this study, we identified 36 potato (Solanum tuberosum L.) genes belonging to the expansin (StEXP) gene family from the genome reference. These genes included 24 α-expansins (StEXPAs), five β-expansins (StEXPBs), one expansin-like A (StEXLA) and six expansin-like B (StEXLBs). The RNA-Seq analysis conducted from a variety of tissue types showed 34 expansins differentially expressed among tissues, some of which only expressed in specific tissues. Most of the StEXPAs and StEXPB2 transcripts were more abundant in young tuber compared with other tissues, suggesting they likely play a role in tuber development. There were 31 genes, especially StEXLB6, showed differential expression under the treatments of ABA, IAA and GA3, as well as under the drought and heat stresses, indicating they were likely involved in potato stress resistance. In addition, the gene co-expression analysis indicated the StEXLBs likely contribute to a wider range of stress resistances compared with other genes. We found the StEXLA and six StEXLBs expressed differently under a range of abiotic stresses (salt, alkaline, heavy metals, drought, heat, and cold stresses), which likely participated in the associated signaling pathways. Comparing with the control group, potato growing under the drought or heat stresses exhibited up-regulation of the all six StEXLB genes in leaves, whereas, the StEXLB3, StEXLB4, StEXLB5 and StEXLB6 showed relatively higher expression levels in roots. This suggested these genes likely played a role in the drought and heat tolerance. Overall, this study has shown the potential role of the StEXP genes in potato growth and stress tolerance, and provided fundamental resources for the future studies in potato breeding.