Heat shock protein 70 (Hsp70) family members play important roles in protecting plants against abiotic stresses, including salt, drought, heat, and cold. In this study, 20 putative StHsp70 genes were identified in potato (Solanum tuberosum L.) through the integration of the gene structures, chromosome locations, phylogenetic relationships, and expression profiles. These StHsp70 genes were classified into five sub-families based on phylogenetic analysis. Chromosome mapping revealed that they were unevenly and unequally distributed on 10 of the 12 chromosomes. Furthermore, segmental and tandem duplication events contributed to the expansion of the StHsp70 genes. Phylogenetic tree of the HSP70 genes from potato and other plant species revealed multiple sub-families. These findings indicated a common ancestor which had generated diverse sub-families prior to a mono-dicot split. In addition, expression analysis using RNA-seq revealed that the majority of these genes were expressed in at least one of the tested tissue, and were induced by Phytophthora infestans. Then, based on qRT-PCR analysis, the results showed that the transcript levels of some of the StHsp70 genes could be remarkably induced by such abiotic and hormone stresses, which indicated their potential roles in mediating the responses of potato plants to both abiotic and biotic stress conditions.