Current methods for determining RNA structure with short-read sequencing cannot capture most differences between distinct transcript isoforms. Here we present RNA structure analysis using nanopore sequencing (PORE-cupine), which combines structure probing using chemical modifications with direct long-read RNA sequencing and machine learning to detect secondary structures in cellular RNAs. PORE-cupine also captures global structural features, such as RNA-binding-protein binding sites and reactivity differences at single-nucleotide variants. We show that shared sequences in different transcript isoforms of the same gene can fold into different structures, highlighting the importance of long-read sequencing for obtaining phase information. We also demonstrate that structural differences between transcript isoforms of the same gene lead to differences in translation efficiency. By revealing isoform-specific RNA structure, PORE-cupine will deepen understanding of the role of structures in controlling gene regulation.