Superthin galaxies are low surface brightness (LSB) disc galaxies, characterized by optical discs with strikingly high values of planar-to-vertical axes ratios (> 10), the physical origin and evolution of which continue to be a puzzle. We present mass models for three superthin galaxies: IC5249, UGC7321 and IC2233. We use high-resolution rotation curves and gas surface density distributions obtained from HI 21 cm radiosynthesis observations, in combination with their two-dimensional structural surface brightness decompositions at Spitzer 3.6 mu m band, all of which were available in the literature. We find that while models with the pseudo-isothermal (PIS) and the Navarro-Frenk-White (NFW) dark matter density profiles fit the observed rotation curves of IC5249 and UGC7321 equally well, those with the NFW profile do not comply with the slowly rising rotation curve of IC2233. Interestingly, for all of our sample galaxies, the best-fitting mass models with a PIS dark matter density profile indicate a compact dark matter halo, i.e. R-c/R-D < 2, where R-c is the core radius of the PIS dark matter halo and R-D is the radial scalelength of the exponential stellar disc. The compact dark matter halo may be fundamentally responsible for the superthin nature of the stellar disc, and therefore our results may have important implications for the formation and evolution models of superthin galaxies in the universe.