The search spans from Stewart Beach to 101st Street.
According to Galveston Island Beach Patrol, the twins were last seen swimming on the west side of the pier, about 20 yards from the shore, at about 4:30 p.m. Sunday.
An hour later, their family called 911 to report the boys missing, adding that while they last saw them in water about waist to chest deep, they never saw them go under.
Along with beach patrol, police, fire and EMS all responded to search the area. Search crews were launched and the U.S. Coast Guard flew its helicopter overnight in hopes of finding the boys.
WATCH: Galveston Beach Patrol's 4:30 p.m. update a day after twins disappear
Galveston Beach Patrol's 4:30 p.m. update a day after twins disappear
The search continued along the shore line and in the water Monday morning. ABC13 crews spotted officials on jet skis searching and diving.
Family members of the missing teens were out at the search site but too distraught to speak on camera. They did, however, share a photo of the boys.
In the meantime, Lt. Austin Kirwin with beach patrol warned about strong currents and waves this time of year in Galveston, advising that people watch their kids closely and look out for jetties and piers in the water.
A lateral current tends to form in the Gulf waters in Galveston.
"Whenever that current hits an object out in the water, such as these jetties, it creates a rip current that forms, which pulls you out to sea away from shore," Lt. Kirwin said. "So, a lot of times, things will get caught in that rip current and they could get stuck on the rocks. They could just get kicked farther out to sea."
Beach patrol said that it's running mobile patrol vehicles and providing 24/7 on-call service.
It added that stationed lifeguards will start working the beach on Saturday, March 11. Lifeguard tryouts will also be held that day.
If you panic and try to fight the current, chances increase that you can drown.
Remember to swim within your limits and near a lifeguard if possible.
Non-swimmers and children should always wear life jackets when in or around the water.