Structural variations (SVs) are a major contributor of genetic diversity and phenotypic variations, however their prevalence and functions in domestic animals are largely unexplored. Here, we assembled 26 haplotype-resolved genome assemblies from 13 genetically diverse sheep breeds using PacBio HiFi sequencing. We then constructed an ovine graph pan-genome and demonstrated its advantage in discovering 142,593 biallelic SVs (Insertions and deletions), 7,028 divergent alleles and 13,419 multiallelic variations with high accuracy and sensitivity. To link the SVs to genotypes, we genotyped the SVs in 687 resequenced individuals of domestic and wild sheep using a graph-based approach and identified numerous population-stratified variants, of which expression-associated SVs were detected by integrating RNA-seq data. Taking the varying sheep tail morphology as example, we located a putative causative insertion in HOXB13 gene responsible for the long tail and reported multiple large SVs associated with the fat tail. Beyond generating a benchmark resource for ovine structural variants, our study also highlighted that the population genetics analysis based on graph pan-genome rather than reference genome will greatly benefit the animal genetic research.