Members refused the scheme because of its impact on the residential amenity of the area and landscape.
The two areas of polytunnels are on a combined area of 14.7 hectares and used for the growing of blackberries and raspberries in plastic grow bags, both as experimental crops.
Raspberry plants are replaced every year while the blackberries are in their second year and expected to produce a crop for a further two to three years.
Herefordshire Council's public rights of way officer objected to any covering of the the public right of way with polytunnel sheeting.
Marden Parish Council wished to see a time limit set on any permission for the polytunnels.
Thirty four letters of objection were received. Main points raised were the polytunnels being unsightly, run-off from fields causing flooding and the polytunnels being close to properties.