The number of people attending at Dewsbury Hospital and Pinderfields Hospital in Wakefield has risen above pre-pandemic levels to around 800 a day, the trust which runs both sites said.
The Mid Yorkshire Hospitals NHS Trust said it was trying to bolster alternatives to A&E for patients who do not need emergency care.
Speaking at a trust board meeting on Thursday, chief operating officer Trudie Davies said: "We have identified a risk that we are experiencing extremely high A&E attendance levels.
"They are now at pre-pandemic numbers-plus.
"So we've got very busy A & E departments, with up to 800 patients per day in those departments."
Ms Davies said that there was a "high proportion of low acuity patients" - people who do not need immediate medical attention - using A & E.
She added: "This is causing a risk of crowding.
"We are looking at our provision to ensure our alternatives to A&E are robust."
A&E attendance at Pinderfields and Dewsbury fell dramatically after the first lockdown was imposed in March 2020, though it did creep back up again over the course of the year.
Last September the trust warned that a return to normal pre-pandemic A & E levels was creating social distancing problems.
Local Democracy Reporting Service