SOUTH HOLLAND, Ill.—Beads of sweat fall from Arturo Martinez's face on a humid afternoon in this suburb south of Chicago while he shouts each movement as he whirls around a Mack semitrailer rig.

He's checking air pressure valves, brakes, tires, fuel levels, lights, gauges—a checklist with hundreds of tasks to be completed before his rig and double trailers are ready to go out on the road.

Mr. Martinez, 28, of Los Angeles, is one of 12 United Parcel Service Inc. employees learning to be a feeder truck driver trainer for the package delivery company. Though much of his 10-year career with UPS has been as a dispatch supervisor, he is learning the ropes of becoming a driver trainer, and part of that means he must complete this inspection in less than 45 minutes with no disqualifications.

The management employees chosen to undergo this rigorous three-week training, which includes hours in the classroom and on the road, are ones that UPS holds to some of its highest safety standards, said Tom Brokop, South Holland, Ill.-based Driver Training School coordinator. The employees—who come from different backgrounds within the company—have to be safe drivers on the road, and must be able to hold and likely raise the bar for future truck drivers at UPS.

“This whole (training program) is all about safety,” said Mr. Brokop, who has been running UPS' feeder truck Driver Training School since 2005. UPS began training its managers to train drivers in the 1960s. “This training protects us from putting the driver and company in an accident situation.”

Each day, students head to the classroom to go over modules on UPS safety standards as well as federal regulations and guidelines. They also review their pre- and post-trip and drill drive performance from the previous day with their trainers, which highlights areas in which they are excelling and those they need to improve to qualify as a driver trainer.

“It's definitely a major challenge,” said Gary Sherman, 60, a supervising dispatcher at a UPS hub in Lexington, Ky. “With the amount of things going on around a driver and the safety standards we have...you have to be aware of everything. We're basically being trained to be solid trainers.”

Mr. Sherman shadows Mr. Martinez with a clipboard and stopwatch as he continues through his pre- and post-trip inspections. Meanwhile, Mr. Martinez ticks off steps on the list with a quick cadence about what he's doing while he's doing it before moving on to the next step.

All seems to be going well until he has to connect one of the two trailers to the rig. As he backs the rig to line it to the trailer, the rig's tires skip a bit and he takes an improper angle.

Mr. Brokop, standing well over 6 feet tall and sporting traditional UPS “browns” and aviator sunglasses, chuckles a bit.

“Nerves,” he said, which may have been frayed given the presence of an extra set of eyes watching him closely. “He normally does this in one shot.”

After Mr. Martinez lines up the first trailer and attaches it to the rig, he must secure the second—a move called coupling. He struggles a bit in his first attempt to line up the rig and first trailer with the dolly of the second trailer, but he soon takes the proper angle to fasten the 3,000-pound dolly to couple the trailers.

This is just the beginning as he prepares to head out for a drill drive in which he will take the truck and double trailers through a 22-mile course of city driving to practice spacing, visibility and turning.

“They really put us to the test out here,” Mr. Martinez said. “We have to apply what we're learning on a daily basis until it becomes second nature. It's beneficial training because it makes us safer drivers, which will then make us better trainers.”