You need to warm them up a bit.
There are a number of ways to do this 20 or 30 seconds on a griddle (or a comal if you have one) wrap a stack in foil and place in 325 oven for until warm wrap a stack in a clean towel and steam them using a steamer slightly moisten a towel and wrap it around a stack and microwave them for a bit If you've warmed them and they are still tearing then
your tortillas are no longer fresh.
cooking.stackexchange.com/users/9799/djmadscribbler
If possible, don't buy your tortillas from a modern super market, but look for a source of homemade/fresh tortillas.
These can be found in many cities in the U.S. at Mexican or Latin American stores or neighboroods.
Perhaps check your yellow pages for "Tortilleria" (The spanish word for "Tortilla Store").
These tortillas will also taste much better (at least in my opinion), and have fewer preservatives or other additives (such as artificial colors, etc).
If you can find a good source of fresh tortillas, they will generally be much softer than those you buy pre-packaged in a supermarket.
They will be fresher, and if you find a good source, they'll be sold to you still warm (often kept in an ice chest or similar, to keep them warm until sale).
If you can't find this, you can learn to make your own tortillas.
Or, you can do as @djmadscribbler suggested, and warm your tortillas gently.
Between warming and using, keep them covered so they don't dry out or cool down.
Don't overheat them, or you'll dry them out (especially if you're warming them individually on the stove).
cooking.stackexchange.com/users/6498/Flimzy
I spread coconut oil on the tortilla (thin layer like butter) and heat them in a hot skillet for about 15 seconds per side, drop it in the enchilada sauce, stuff and roll.
That way the tortilla gets pliable, the sauce gets on the tortilla, and the sauce helps it stick together and look nice and neat.
I've tried many ways (enchiladas are one of my favorite dinners to make with leftover beef or chicken) and this one has proven to be the easiest for me.
cooking.stackexchange.com/users/10250/Jessica
My husband is Mexican grew up in Puebla, Mexico, the proud "mecca" of Mexican cuisine.
His family puts their corn tortillas in a plastic grocery bag and microwaves them for a few seconds.
Or, they warm them in a frying pan in olive oil for a few moments on each side, long enough to soften but not crisp them.
I've never seen Poblano cuisine use crispy tortillas.
cooking.stackexchange.com/users/17697/Gringuita
i have kind of given up on having perfect store bought corn tortillas.
so i decided to just layer them all across the bottom of a casserole dish and then filling
and then all across the top with whatever sauce and cheeses you want to add.
almost lasagna like.
i know its fake bu i slice them in enchilada size portions.
no one knows the difference.
cooking.stackexchange.com/users/52490/Tracy Sharp
I used to make enchiladas all the time and what I did was dip the corn tortilla in hot oil briefly, flip and do it again.
However, now the tortillas I get turn mushy and tear easily, so I think something about the tortillas in my neightborhood has changed.
A friend's family's technique is to fry them in oil until they are almost hard enough for tostadas since she explained that the enchilada sauce will soften the tortillas once they are cooked.
cooking.stackexchange.com/users/17609/Candace
Using tongs, dip corn tortillas in hot manteca (lard) briefly on both sides, and drain on paper towels.
cooking.stackexchange.com/users/24615/Tex-Mex Gerry
Just made a large pan of chicken enchiladas.
Heated the corn tortillas in a small, dry skillet (no oil).
This is the first time I have not either dipped them in enchilada sauce or fried in oil.
Was able to easily roll them, except for repeatedly burning my fingers.
:o
( I think I prefer the dry way, as I'd rather not add additional calories if I don't have to.
[Note: the tortillas were pretty fresh, which I do believe helped.]
cooking.stackexchange.com/users/33998/Kim
I like the flavor and texture of corn tortillas (store-bought), but they always tear apart whenever I try to use them in a non-flat way - enchilada-style, for example.  How can I make the corn tortillas soft enough to work with (to roll around some ingredients, for example)?
How can I get a corn tortilla to be pliable enough to work with?
cooking.stackexchange.com
<mexican-cuisine><tortilla>
cooking.stackexchange.com/questions/23532
cooking.stackexchange.com/users/1685/KatieK
You can wrap a moist towel around them and microwave them, pan fry them briefly on both sides with or without lard, wrap in a clean towel and steam them in a steamer, wrap in foil and warm them in the oven, or dip them in hot lard and drain on paper towels. You should warm them up. You can do this in a skillet or a grill or in a microwave.
You need to warm them up. You can do this on a griddle, in a skillet or briefly in hot oil. You can heat them up for a few seconds in the microwave.