Starch degradation provides energy and signaling molecules for plant growth, development, defense, and stress response. α-amylase (AMY) is one of the most important enzymes in this process. Potato tubers are rich in starch, and the hydrolysis of starch into sugar negatively impacts the frying quality of potato. Despite its importance, the AMY gene family has not been fully explored in potatoes. Here, we performed a detailed analysis of the StAMY gene family to determine its role in potato. Twenty StAMY genes were identified across the potato genome and were divided into three subgroups. The promoters of StAMY genes contained an array of cis-acting elements involved in growth and development, phytohormone signaling, and stress and defense responses. StAMY8, StAMY9, StAMY12, and StAMY20 were specifically expressed in mature tubers. Different StAMY gene family members tended to be upregulated in response to β-aminobutyric acid (BABA), Phytophthora infestans (P. infestans), benzothiadiazole (BTH), heat, salt, and drought stress. In addition, different StAMY gene family members tended to be responsive to abscisic acid (ABA), indole-3-acetic acid (IAA), gibberellic acid (GA3), and 6-benzylaminopurine (BAP) treatment. These results suggest that StAMY gene family members may be involved in starch and sugar metabolism, defense, stress response, and phytohormone signaling. The results of this study may be applicable to other starchy crops and lay a foundation for further research on the functions and regulatory mechanisms of AMY genes.