  From radio and higher-frequency observations, more than 300 SNRs have been
discovered in the Milky Way, of which 220 fall into the H.E.S.S. Galactic Plane
Survey. However only 50 SNRs are coincident with a H.E.S.S source and in 8
cases the VHE emission is firmly associated with the SNR. The H.E.S.S. dataset
includes now more than 8 years of observations and it is of great interest to
extract VHE flux upper limits from undetected SNRs. These new measurements can
then be used to test the standard paradigm of the SNRs as the origin of
Galactic cosmic rays. In this contribution, the H.E.S.S. results on the
population of SNRs and the subsequent constraints on the cosmic-ray
acceleration efficiency in these sources will be presented.
