Drought is one of the most significant limiting factors affecting plant growth and development on the Qinghai–Tibet Plateau (QTP). Mining the drought-tolerant genes of the endemic perennial grass of the QTP, Siberian wildrye (Elymus sibiricus), is of great significance to creating new drought-resistant varieties which can be used in the development of grassland livestock and restoring natural grassland projects in the QTP. To investigate the transcriptomic responsiveness of E. sibiricus to drought stress, PEG-induced short- and long-term drought stress was applied to two Siberian wildrye genotypes (drought-tolerant and drought-sensitive accessions), followed by third- and second-generation transcriptome sequencing analysis. A total of 40,708 isoforms were detected, of which 10,659 differentially expressed genes (DEGs) were common to both genotypes. There were 2107 and 2498 unique DEGs in the drought-tolerant and drought-sensitive genotypes, respectively. Additionally, 2798 and 1850 DEGs were identified in the drought-tolerant genotype only under short- and long-term conditions, respectively. DEGs numbering 1641 and 1330 were identified in the drought-sensitive genotype only under short- and long-term conditions, respectively. Kyoto Encyclopedia of Genes and Genomes (KEGG) enrichment analysis revealed that all the DEGs responding to drought stress in E. sibiricus were mainly associated with the mitogen-activated protein kinase (MAKP) signaling pathway, plant hormone signal transduction, the linoleic acid metabolism pathway, the ribosome pathway, and plant circadian rhythms. In addition, Nitrate transporter 1/Peptide transporter family protein 3.1 (NPF3.1) and Auxin/Indole-3-Acetic Acid (Aux/IAA) family protein 31(IAA31) also played an important role in helping E. sibiricus resist drought. This study used transcriptomics to investigate how E. sibiricus responds to drought stress, and may provide genetic resources and references for research into the molecular mechanisms of drought resistance in native perennial grasses and for breeding drought-tolerant varieties.