Taylor Swift and Travis Kelce's celebration kept guests waiting when it came time to eat ... TMZ has learned attendees stood in long buffet lines ... some even ate on their feet because there weren't enough seats.

Sources who attended the party tell TMZ ... there was no formal sit-down dinner. Instead, guests lined up at multiple buffet-style food stations before searching for one of the limited seats available.

One source summed up the dinner scene by telling TMZ it was "a bit of a s*** show" because there were simply too many people and not enough places for everyone to sit.

Still, our sources say nobody went hungry. Guests had their pick of an extensive spread, with stations serving everything from pasta and sushi to chicken, salads, filet mignon, and a mix of Chinese, Italian, and American favorites. Employees staffed every food station, serving food directly onto guests' plates.

And dessert was just as over-the-top. We're told there was a massive dessert table featuring around 30 different cakes, each topped with a unique 3D figure of Taylor and Travis. There were also all kinds of other desserts for guests to choose from.