In the human genome, it has been estimated that considerably more sequence is under natural selection in non-coding regions [such as transcription-factor binding sites (TF-binding sites) and non-coding RNAs (ncRNAs)] compared to protein-coding ones. However, less attention has been paid to them. To study selective pressure on non-coding elements, we use next-generation sequencing data from the recently completed pilot phase of the 1000 Genomes Project, which, compared to traditional methods, allows for the characterization of a full spectrum of genomic variations, including single-nucleotide polymorphisms (SNPs), short insertions and deletions (indels) and structural variations (SVs). We develop a framework for combining these variation data with non-coding elements, calculating various population-based metrics to compare classes and subclasses of elements, and developing element-aware aggregation procedures to probe the internal structure of an element. Overall, we find that TF-binding sites and ncRNAs are less selectively constrained for SNPs than coding sequences (CDSs), but more constrained than a neutral reference. We also determine that the relative amounts of constraint for the three types of variations are, in general, correlated, but there are some differences: counter-intuitively, TF-binding sites and ncRNAs are more selectively constrained for indels than for SNPs, compared to CDSs. After inspecting the overall properties of a class of elements, we analyze selective pressure on subclasses within an element class, and show that the extent of selection is associated with the genomic properties of each subclass. We find, for instance, that ncRNAs with higher expression levels tend to be under stronger purifying selection, and the actual regions of TF-binding motifs are under stronger selective pressure than the corresponding peak regions. Further, we develop element-aware aggregation plots to analyze selective pressure across the linear structure of an element, with the confidence intervals evaluated using both simple bootstrapping and block bootstrapping techniques. We find, for example, that both micro-RNAs (particularly the seed regions) and their binding targets are under stronger selective pressure for SNPs than their immediate genomic surroundings. In addition, we demonstrate that substitutions in TF-binding motifs inversely correlate with site conservation, and SNPs unfavorable for motifs are under more selective constraints than favorable SNPs. Finally, to further investigate intra-element differences, we show that SVs have the tendency to use distinctive modes and mechanisms when they interact with genomic elements, such as enveloping whole gene(s) rather than disrupting them partially, as well as duplicating TF motifs in tandem.