Elastic constants of two-dimensional soft cyclic trimers, exhibiting asymmetry and atomic size dispersion, are studied at zero temperature. The molecules interact through a short-range, site–site, purely repulsive, n-inverse-power potential. The essential influence of the molecular asymmetry on the elastic properties is shown. Negative values of the Poisson’s ratio are found for strongly asymmetric molecules. It is also shown that, at fixed number density in the system, by increasing the size dispersion of particles one can significantly increase the elastic constants and the Poisson’s ratio.