Drogheda Homeless Aid provides a 29-bed hostel for men in the Co Louth and Co Meath areas.
Around 140 people come through the door each year.
Manager Tracy McAuley said during the cold weather, they can also take rough sleepers in from the streets.
Camp beds have been set up in the hostel's communal TV room and the hostel has increased its capacity by turning some single rooms into doubles.
"There isn't anywhere to move anybody on. We're full. We have 33 residents at the moment. We can't take any more," she said.
"But as long as we don't move people on, we can't create a space for the next person," she added.
Ms McAuley said constraints in social and affordable housing, and the private rental market has caused people to stay longer in the hostel.
She said: "Even though we're supposed to be emergency accommodation, people have nowhere to move on to.
"And we don't have anywhere to move them on to."
Ms McAuley said demand for services was such that she could build the hostel three times over and fill it all.
"We are constantly taking people in from the streets. We recently took in two men, who were living separately, living in their cars," she said.
She said one of her biggest concerns is the number of families and children entering homelessness.
Drogheda Homeless Aid has a small number of houses for families and "transitional housing" where people are supported to move on from the hostel towards independent living.
One of those people is Michael, who became homeless two years ago after returning home from living abroad for several years.
He said he bought a van and lived in it for a few months, before coming to the hostel.
"I got so cold and depressed, I knew I had to get out of that," he said.
Michael said he has been in recovery from drug and alcohol addiction and is now "19 years clean and sober," adding the hostel and the people there saved his life.
He is now living in transitional housing which offers him more freedom than the hostel, but he is ready to move out, if he can get somewhere to live.
"I hope to get a little one bed townhouse with a yard and space for a dog and a canary. I'm 64 years old," he said.
He can stay in his current accommodation for 18 months.
"If I don't get housed in the 18 months, I'll have to come back here, if I'm lucky. If not, I'll be back on the road, the street again".
