Polish truck drivers and farmers extended the blockade to the Medyka border crossing last week, one of the busiest crossings with Ukraine.
Four border crossings are now blocked in total, in the protest that began on November 6.
Polish truck drivers say they are unfairly disadvantaged since their Ukrainian counterparts do not have to pay for permits to enter the EU. They want the requirements to be reinstated.
2,700 trucks stuck at the border
The queues are growing, and so is the discontent among Ukrainian truckers.
"The procedure that used to take 10 to 15 hours now takes a week," said Igor, a Ukrainian truck driver stuck at the border. "So it's not easy. The conditions are inhuman."
Ukrainian media reported that two Ukrainian drivers, aged 54 and 56, died of natural causes while in the queue at the border.
The same sources said essential goods, such as humanitarian aid are being delayed, in spite of earlier promises by Polish truckers that the blockade would apply only to non-essential goods.
Ukrainian officials and industry representatives said the demands are unrealistic, with some even pointing to strong pro-Russian sentiment among Polish protesters.