SNRs are likely to be significant sources of Galactic cosmic rays up to the knee. They produce gamma rays in the very-high-energy ($E>100$~GeV) range mainly via two mechanisms: hadronic interactions of accelerated protons with the interstellar medium and leptonic interactions of accelerated electrons with soft photons. Observations with current instruments have lead to the detection of about a dozen SNRs in VHE gamma rays and future instruments will help significantly increase this number. Yet, the details of particle acceleration at SNRs, and of the mechanisms producing VHE gamma-ray at SNRs remain poorly understood: What is the spectrum of accelerated particles? What is the efficiency of particle acceleration? Is the gamma-ray emission dominated by hadronic or leptonic origin?

To address these questions, we simulate the population of SNRs in the gamma-ray domain, and confront it to the current population of TeV SNRs. This method allows us to investigate several crucial aspects of particle acceleration at SNRs, such as the level of magnetic field around SNR shocks or scanning the parameter space of the accelerated particles (spectral index, electron to proton ratio and the acceleration efficiency of the shock) with the possibility to constrain some of the parameters.