Prospects on searches for new physics at the high-luminosity LHC are presented for the ATLAS and CMS experiments. Two integrated luminosity scenarios are assumed : 300 fb$^{-1}$, corresponding to the end of the LHC run 3, and 3000 fb$^{-1}$, the integrated luminosity expected to be collected during the LHC phase 2. Results for strongly produced and weakly produced supersymmetric particles are first detailed. A selection of results on searches for new physics beyond the standard model is then given, in particular the search for heavy resonances in various decay channels and the search for dark matter candidates.