Wanda and Randy Bliek awoke on Saturday to the sound of water lapping against the walls of their home in Rock Valley, Iowa.

The couple rushed to their pickup truck and drove onto the street, but surging water pushed them against the curb. Unable to open the truck doors, they said, they escaped through the windows and climbed out into the neck-high current gushing down their street.

For eight long blocks, they alternated between swimming and walking to safety while neighbors screamed for help from their roofs. At one point, Ms. Bliek, 65, told her husband she was not sure she could continue.

“I said, ‘Well, if you want to stay alive, we’ve got to do this,’” Mr. Bliek recalled.

Rock Valley, a town of 4,000 people in northwest Iowa, was among the hardest-hit places in a weekend of severe flooding that destroyed homes, inundated farm fields and left residents scrambling to evacuate in three Midwestern states.

As a new week started, and as the floods retreated in some places, danger persisted. Along the Big Sioux River in North Sioux City, S.D., where the water reached record levels, a key railroad bridge collapsed late Sunday night. In southern Minnesota, a dam was at risk of failing on Monday.