Sag Harbor supermodel Christie Brinkley says posing with her daughters for the new Sports Illustrated Swimsuit issue harkens back to her own fledgling days as a model.

“This is a real full-circle moment for me,” Brinkley, 63, says in a promotional video on the Sports Illustrated website shot during the photo session at a tropical seaside. “And I can get very emotional about this,” she added with a laugh. “I really can.”

Choking back tears, she mused, “How many years ago I was that insecure girl and hoping that I would be good enough for the magazine. So to see my daughters now having the same thoughts that I had and to be able to see them actually be there on the job, [is] like, definitely a big moment.”

Brinkley and her daughters — singer Alexa Ray Joel, 31, with her second husband, music legend Billy Joel, and Sailor Brinkley Cook, 18, with her fourth husband, architect Peter Cook — posed together and separately in bikinis and posted images on Instagram, where the two young women spoke of, among other things, body insecurity.

“I’ve had issues with my body image since before I can even remember,” wrote Brinkley Cook, an IMG model and a student at Parsons School of Design. “I grew up not loving how I looked and felt held back because of it. I don’t know why I always felt that way, sure I had baby fat and definitely went through a plethora of awkward phases, but I had a family that loved me i had friends who made me laugh etc. But for some reason I still looked in the mirror and always somehow found something to pick on. I went from being ‘too fat’ to ‘too thin’ to ‘too muscular’ and I never felt satisfied. My body and I have been through it all. But recently I have been liberated. I am healthy, i treat myself well, and for that i’m happy.”

Though Joel wrote, “I don’t have a completely flat tummy, or cellulite-free thighs,” neither imperfection was visible in the photos by Emmanuelle Hauguel. Regardless, the singer urged, “Let’s STOP degrading and START celebrating ourselves and others, from both the inside AND out. There’s far too much degradation, competition, insecurity, and unhealthy standards associated with women and their bodies -- particularly on social-media. … All that matters is how YOU feel about yourself. Set your own standards of beauty; both internally and externally. All of those unrealistic-looking, photoshopped images are nothing more than white noise, playing off of your own insecurities in order to make a buck. Don’t let them affect you.”

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Brinkley — who first landed the cover of the swimsuit issue in 1979, then again on the covers for 1980 and ’81 — said her daughters’ encouragement motivated her to return to posing in a bikini.

“My first thought was, ‘At my age? No way!’ ” she told People magazine. “When I turned 30, I was like, ‘This is the last time I’m posing in a bathing suit!’ When this issue comes out, I’ll be 63. I thought, ‘Those days are over.’ But to get to do it with my girls, I thought, ‘One last go!’ ”