Background Three-dimensional spatial organization of chromosomes is defined by highly self-interacting regions 0.1-1 Mb in size termed Topological Associating Domains (TADs). Genetic factors that explain dynamic variation in TAD structure are not understood. We hypothesize that common structural variation (SV) in the human population can disrupt regulatory sequences and thereby influence TAD formation. To determine the effects of SVs on 3D chromatin organization, we performed chromosome conformation capture sequencing (Hi-C) of lymphoblastoid cell lines from 19 subjects for which SVs had been previously characterized in the 1000 genomes project. We tested the effects of common deletion polymorphisms on TAD structure by linear regression analysis of nearby quantitative chromatin interactions (contacts) within 240 kb of the deletion, and we specifically tested the hypothesis that deletions at TAD boundaries (TBs) could result in large-scale alterations in chromatin conformation. Results Large (> 10 kb) deletions had significant effects on long-range chromatin interactions. Deletions were associated with increased contacts that span the deleted region and this effect was driven by large deletions that were not located within a TAD boundary (nonTB). Some deletions at TBs, including a 80 kb deletion of the genes CFHR1 and CFHR3, had detectable effects on chromatin contacts. However for TB deletions overall, we did not detect a pattern of effects that was consistent in magnitude or direction. Large inversions in the population had a distinguishable signature characterized by a rearrangement of contacts that span its breakpoints. Conclusions Our study demonstrates that common SVs in the population impact long-range chromatin structure, and deletions and inversions have distinct signatures. However, the effects that we observe are subtle and variable between loci. Genome-wide analysis of chromatin conformation in large cohorts will be needed to quantify the influence of common SVs on chromatin structure.