Drivers are being asked to stay away from Coombes Farm until the weather improves.
Lambing is going well but the rain has meant the fields are too muddy to open for parking.
With limited space on the roads, farmer Jenny Passmore has had to put out a plea asking visitors to wait until the weather is better.
She said: “It is a nightmare. The last time it was anywhere as near as wet as this was in 2001 and that was the year of foot and mouth. I remember then because they were trapped in the field.
“It is not as bad as that but all the while I have been doing the farm tours, I have never had it so wet. It is such a shame.
“Some people have walked over from Lancing, and we have had some lovely visitors, but a lot of people have stayed away.
“We haven’t had any moans, they all appreciate what we are going through. We just ask people to park sensibly so the emergency services can get through and people have been parking well, down at Passies Pond, then walking up.
“We still welcome people, of course, we just can’t park them.”
It has been a bit of a strange lambing season, starting in March in the snow, but there have been lots of births, including some unusual ones.
Jenny said: “We started off with snow. People were bringing their toboggans, so instead of tractor rides we had tobogganing.
“We have got a really good team of farming students helping and the late-night lambing has carried on as normal because the numbers are limited. It is the third year and it is fully booked.
“The lambing is good, we have got loads of lambs and we have had two sets of quins, which is really unusual, but we can’t put any of them out because the fields are too wet.
“If we get a dry day, we can put them out if they are strong, as they will be okay, but we can’t put them out if they are weak, so we have loads of ewes and lambs in the barns. Any spare space has a sheep in it. We are also having to feed them because the grass has been affected.”
Coombes Farm will be open to visitors until Sunday, April 15, 9.30am to 4pm. Admission is £3 for adults, £2 children. Tractor rides, when they can run, are £2.50 a head.