First searches for physics beyond the Standard Model at CMS

We present an overview of the searches for new physics beyond the Standard Model at the CMS experiment with early data delivered by the LHC at 7 TeV. We discuss especially the results for new resonances in dijet events and long-lived heavy particles. Some results, like the search for Stopped Gluinos, already extend the existing limits from Tevatron although no evidence of new physics has been observed with the first 0.1-1.1 inverse picobarn recorded. More statistics are needed to study the kinematics phase-space where SUSY signal is expected, so the emphasis is put on testing the methods for supressing and measuring the SM background, using data-driven techniques.