The United Nations says more than 800,000 people have left Ukraine since the Russian invasion began.
Most of the tens of thousands crossing into Poland stay with relatives or move on to other countries, but others have nowhere to go.
Some people living near the border are opening their homes to those who need shelter. The BBC’s Mark Lowen met Joanna, a mother of three, as she welcomed Anna and her five-year-old daughter, Milena, after they had fled from Kyiv.