The propensity to acquire mutations depends on the oligonucleotide context of a DNA locus. In turn, this differential mutability of oligonucleotides varies across individuals due to exposure to mutagenic agents or due to variable efficiency of DNA repair pathways. Such variability is captured by mutational signatures, mathematical constructs resulting from a deconvolution of mutation frequency spectra across individuals. There is a need to enhance methods for inferring mutational signatures to make better use of sparse mutation frequency data that results from genome sequencing, and additionally to facilitate insight into underlying biological mechanisms. In cancer genomics, novel approaches to analyze somatic mutation patterns may help explain the etiology of various tumor types, as well as provide a more accurate baseline to infer positive and negative selection on somatic changes that drive tumor evolution. We propose a conceptualization of mutational signatures that represents oligonucleotides via descriptors of DNA conformation: base pair, base pair step, and minor groove width parameters. We demonstrate how such DNA structural parameters can accurately predict mutation occurrence due to DNA repair failures or due to exposure to diverse mutagens, including radiation, chemical exposure and the APOBEC cytosine deaminase enzymes. Furthermore, the mutation frequency of DNA oligomers classed by structural features can accurately capture systematic variability in mutational spectra of >1,000 tumors originating from diverse human tissues. Overall, we suggest that the power of DNA sequence-based mutational signature analysis can be enhanced by drawing on DNA shape features.