Water poured into hospitals. Ambulances were caught up in roiling floodwaters. Medical transport helicopters were grounded by high winds. Houston’s world-renowned health care infrastructure found itself battered by Hurricane Harvey, struggling to treat storm victims while becoming a victim itself.

The coming days will inevitably bring more hazards for storm-damaged hospitals and nursing homes, and their patients and staff. The scenes of turmoil across Texas raised the specter of the extreme flooding following Hurricane Katrina in 2005, when dozens of hospital and nursing home patients died, and doctors awaiting rescue at one stranded, powerless hospital became so desperate, they intentionally hastened the deaths of their patients.

The response to Harvey, now a tropical storm but still wreaking havoc over the state, promises answers to whether health officials learned lessons from the catastrophe of Katrina when it comes to the medically vulnerable — in particular whether they did enough to prepare for the disaster and to move patients out of its path.

“We’ve made significant investments,” Dr. Umair Shah, executive director of Harris County’s public health department, said in a telephone interview on Sunday. “The challenge is until it unfolds there’s so many moving pieces and it’s never the same as the situations you’ve previously encountered.”

Responders point to dozens of improvements, from better engineered structures to well-practiced cooperation, that are helping protect lives. Still, sometimes even the soundest plans have been foiled.

Water rose in the basement of Ben Taub Hospital, a major county trauma center in the vast Texas Medical Center campus that had spent billions of dollars on flood protections after being devastated in Tropical Storm Allison in 2001. Officials announced an evacuation Sunday, but hours later, a hospital spokesman said it had not yet begun because the hospital was surrounded by water and rescuers could not reach its 350 patients. On Monday afternoon, a call went out on local radio for a vendor to provide food for the hospital.

As of Monday afternoon, 10 to 15 other hospitals and various nursing homes, some in rural communities, have also evacuated or begun evacuating since the storm made landfall, said Darrell Pile, chief executive of the Southeast Texas Regional Advisory Council, which established a catastrophic medical operations center in Houston’s emergency command center. At one hospital in northwest Houston, CHI St. Luke’s Health — the Vintage, patients were transported by airboat to nearby ambulances due to severe flooding from the Cypress Creek. As displaced residents filled the George R. Brown Convention Center, the city sent out a call for licensed health workers to help people with medical needs there.

While some vulnerable hospitals and nursing homes opted to move their patients out of the region in the hours before the storm, Mr. Pile said, others “did not know to necessarily expect this level of chaos.” A large coalition of medical providers had drilled and planned regularly for catastrophes, he added, “but honestly, not at this epic level.”

Most hospitals in Houston continued operating and they reported that they were doing well. But some, ringed by floodwater, were cut off from patients trying to reach them. Hospital staff members had trouble getting to work as well.

In other parts of the state, Harvey knocked out utilities, forcing hospitals to rely on vulnerable backup systems. The wind and rain were threatening at Citizens Medical Center in Victoria, a city of about 68,000 people roughly 125 miles southwest of Houston, when emergency workers loaded patients onto a mass evacuation ambulance while roads were passable late Saturday night. Amid the stressful scene, one older woman clutched a brown teddy bear while waiting to be taken aboard.