It comes after an angler was forced to scale a cliff face to escape a colony of aggressive seals he encountered on a beach.
Grey seals come ashore to give birth in autumn and winter, and people are urged to stay away from them and keep dogs on leads.
The Scottish SPCA expects to care for more than 100 grey seal pups over the course of the autumn/winter season.
Scottish SPCA spokesman Colin Seddon said: “Grey seals come ashore to give birth in autumn and winter, which is why we see such an increase at this time of year.
“We are urging the public not to approach seal pups which have come ashore and to keep dogs on a lead in case they frighten them into the water.
“If you spot a pup with a white coat on a public beach, please contact our animal helpline as chances are, it is in trouble and needs our attention.
“Grey seal pups which no longer have a white coat may still need our assistance if they are on a public beach for more than four hours or have visible signs of injury, such as bleeding, glued together eyes or generally looking unwell.
“The public should contact our animal helpline and an operator will be able to assess the situation.”
On Friday, a man was rescued from a cliff face in darkness after he was forced to flee a colony of aggressive seals.
Around 50 of the mammals and their young pups turned on the angler as he walked along the beach near Eyemouth.
He scrambled up the cliff face in Green Stane in the Scottish Borders but got trapped about three-quarters of the way up.
Emergency services called to the scene at about 7.40pm used rope rescue techniques to lower a coastguard officer 75ft to where the man was stuck on the cliff face.
An RNLI lifeboat waiting offshore then managed to nip in among the seals to reach the angler and cliff technician, before taking them to Eyemouth Harbour.