Three new kinds of molecular networks are designed and predicted to exhibit negative Poisson ratios. Molecular mechanics calculations on these networks show that the magnitude of Poisson ratios depends on the relative flexibility of beam and arm structures. Several new kinds of auxetic polymers, whose successful synthesis should be easier than that of the corresponding auxetic networks, are then proposed. It is found that the kabob-like polymers with auxegens lying vertically on the main chain can acquire auxeticity while those with auxegens lying horizontally on the main chain cannot. Besides, a half kabob-like or pseudo-ladder polymer with auxegens linked at the intersection of the beam and the arm does show auxeticity when adopting constrictive conformers. It is, however, worthwhile noting that the origins of auxeticity still await and strongly deserve further experimental and theoretical investigations. Three new kinds of molecular networks are designed and predicted to exhibit negative Poisson ratios. Molecular mechanics calculations on these networks show that the magnitude of Poisson ratios depends on the relative flexibility of beams and arm structures. Several new kinds of auxetic polymers, whose successful synthesis It is found that the kabob-like polymers with auxegens lying vertically on the main chain can acquire auxeticity while those with auxegens lying horizontally on the main chain can not. Besides, a half kabob-like or pseudo-ladder polymer with auxegens linked at the intersection of the beam and the arm does show auxeticity when adopting constrictive conformers. It is but, worthwhile noting that the origins of auxeticity still await and strongly deserve further experimental and theoretical investigations.