One strategy to avoid rapid degradation of small nucleic acids in biomedical applications is to covalently link their 3'- and 5'-ends, turning them into circular nucleic acids (circNAs). Here, we examine structural properties of flexible non-base-paired circNAs, containing 6-48 nucleotides, in aqueous solution, using microsecond long molecular dynamics simulations. Analyses of conformational ensembles of circular DNA (circDNA) and RNA (circRNA) molecules of different lengths and sequences reveal how their structures and dynamics are affected by the constraints of their geometries. The circDNAs are more bent and flexible than circRNAs, with distinctly different arrangements of phosphate backbones and bases. Small circNAs can sequester counterions in conformations that resemble crown ethers for the smallest (6-8 nucleotide long) molecules examined, in contrast to their linear counterparts. At millimolar concentrations (7.9 mM), circNA molecules were observed to aggregate, adopting linear chain shapes at physiological ionic strengths.