In this paper we present a new Monte Carlo event generator ReneSANCe for simulation of processes at electron-positron colliders. In the current release of the generator the Bhabha scattering (e+e−→e−e+) and Higgs-strahlung (e+e−→ZH) process are implemented. Based on the SANC (Support for Analytic and Numeric Calculations for experiments at colliders) modules, the new generator takes into account complete one-loop and some higher-order electroweak radiative corrections with finite particle masses and polarizations. The new generator effectively operates in the collinear region and at the ZH production threshold. It is constructed in such a way that new processes can be easily added. The paper contains a theoretical description of the SANC approach, numerical validations and manual.