Below, you’ll find the foul ball rules. At the bottom of the page, you’ll see that I’ve simplified them for you:

MLB Rules General Overview:

A FOUL BALL is a batted ball that settles on foul territory between home and first base, or between home and third base, or that bounds past first or third base on or over foul territory, or that first falls on foul territory beyond first or third base, or that, while on or over foul territory, touches the person of an umpire or player, or any object foreign to the natural ground.
A foul fly shall be judged according to the relative position of the ball and the foul line, including the foul pole, and not as to whether the infielder is on foul or fair territory at the time he touches the ball.

Rule 2.00 (Foul Ball) Comment: A batted ball not touched by a fielder, which hits the pitcher’s rubber and rebounds into foul territory, between home and first, or between home and third base is a foul ball.

FOUL TERRITORY is that part of the playing field outside the first and third base lines extended to the fence and perpendicularly upwards.

A FOUL TIP is a batted ball that goes sharp and direct from the bat to the catcher’s hands and is legally caught. It is not a foul tip unless caught and any foul tip that is caught is a strike, and the ball is in play. It is not a catch if it is a rebound, unless the ball has first touched the catcher’s glove or hand.

The rules that most specifically discussion foul balls are: The Runner (07_the_runner) and The Official Scorer (10_the_official_scorer).

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The rules can be a bit confusing to many. Let’s see if I can simplify things:

A foul ball is anything outside the baselines. It can be a pop-up, a line drive, a grounder. If it isn’t between the lines for the baselines, it’s a foul ball.

A foul ball can count as a Strike 1 and a Strike 2, but never a Strike 3.

A foul ball pop-up/fly ball is treated the same as any ball hit inside the lines. This means if a runner is on base, he can tag up and risk running to the next bag. This includes scoring, if it is an option. This is only the case for fly balls though. Once the ball hits the ground in foul territory, the play is dead.

A foul tip is not the same as a foul ball. It is counted, essentially, as a swing and miss. Thus, you will sometimes see the ump make a sweeping gesture off his fingertips. This indicates a foul tip for a strike. It can be counted as a third strike.