Generous people have been playing Santa and dropping off gifts for two Victorian families whose gifts were stolen from under their Christmas trees.

Police at Wodonga near the Victoria-NSW border are calling the thefts “an unthinkable act of heartlessness”.

But they say they have been overwhelmed by the number of donated presents that have been arriving at the police station throughout Christmas Day.

The Salvation Army also gave presents to the children at one of the homes.

“The occupants of the houses were asleep and realised all their gifts were missing when they went to open them this morning,” a police spokeswoman said.

The two homes are on different streets, Wilca Way and Hartwig Road, on the southern end of the town.