Structural characteristics are essential for the functioning of many noncoding RNAs and cis-regulatory elements of mRNAs. SNPs may disrupt these structures, interfere with their molecular function, and hence cause a phenotypic effect. RNA folding algorithms can provide detailed insights into structural effects of SNPs. The global measures employed so far suffer from limited accuracy of folding programs on large RNAs and are computationally too demanding for genome-wide applications. Here, we present a strategy that focuses on the local regions of maximal structural change between mutant and wild-type. These local regions are approximated in a "screening mode" that is intended for genome-wide applications. Furthermore, localized regions are identified as those with maximal discrepancy. The mutation effects are quantified in terms of empirical P values. To this end, the RNAsnp software uses extensive precomputed tables of the distribution of SNP effects as function of length and GC content. RNAsnp thus achieves both a noise reduction and speed-up of several orders of magnitude over shuffling-based approaches. On a data set comprising 501 SNPs associated with human-inherited diseases, we predict 54 to have significant local structural effect in the untranslated region of mRNAs. RNAsnp is available at https://rth.dk/resources/rnasnp. Structural characteristics are essential for the functioning of many non-coding RNAs and cis-regulatory elements of mRNAs. Predictions of the significance of sequence variants on structural effects were made using RNAsnp on a dataset of 30 known SNPs reported to have a structural effect. The four experimentally validated SNPs were correctly predicted with this application (p-value <0.1).