Specifically a Deluxe Series Strat HSS?

WOW. Who are you Stevie Ray Vaughn? Just kidding. No it won't resist but you will need a good setup if you've been using .09's or .010's. When you put the .013's on and tune it. You may notice a difference in string height. If you have a floating trem it's gonna really jack it up.

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"Damn Right I Got the Blues"

You will have to adjust your spring tension , you truss rod to deal with the extra tension from such heavy strings. You may have to redo your intonation. Not to hard may take a nite to sort out and then check to see if it needs adjustment

I got as far as 12s tuned down a full step but have been settled with using 11s tuned to standard 440 for a long while now, no floating trem to deal with but still got it loaded with five springs for stability, sustain.
try a set of 12s first "Ernie Ball - Not even Slinky's" an see how they go.
That would be my advice.

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Dan...

Fender 1987 MIJ Stratocaster, Texas Special Loaded.
Fender 2007 MIA Jazz Deluxe.

Yeah, I tried 12's for a while but decided they weren't for me so settled on 11's.

No reason your Strat won't cope with them though - your fingers might be a different story lol!!

What sort of music are you playing?

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How did it sound to you?

Unless you've been playing for a long time don't go to 13's. If you're a beginner and want to use 13's because your favorite guitarist does, DON'T. 13's are hard to play and if you're still learning how to play using 13's will only hurt your development. I'm speaking from personal experience.

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Tune Low, Play Hard & Floor it!

There should be no issues with 13's. Just make sure you do a complete setup.

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Chet Feathers

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I didn't Lose my mind, I traded it for this guitar.

.13's won't hurt your axe, YOU on the other hand.....that's a different story LOL. Like almost everyone else said, you guitar will require a complete setup after putting those .13's on there. If you are just looking for TONE, I think .11's would do just fine. Heck, even .10's begin to make a strat sing! I think you may find that .13's will be so stiff, it will essentially make your guitar useless (except for slide guitar LOL) Seriously though, a good set up, and good luck friend!

Strats are no stranger to heavy guage strings since they came stock from the factory with at least 12's in the 50's and 60's. Maybe they even shipped with 13's?

But like others said, you'll need to do a complete setup after slapping on those piano wire-like 13's; truss rod, action, intonation, pickup height...
The only out of the oridinary work I can think of is you might need to widen the nut slots so the 13's won't bind (forget about going back to 10's or below after do that) and you might need stiffer trem springs. The Am Deluxe comes with 3 of those wimpy modern black springs. You might need to change them to the stiffer vintage type springs and/or add more springs while you crank the trem claw in to keep the bridge from raising up into the sky.

Good luck with the 13's and enjoy your new calluses

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Obligatory gear list: Fender, Rickenbacker, Gibson, Gretsch, Vox, Martin, and more Fender.

Unless you use your trem, i don't so Ive got mine loaded my with five springs, medium action an 11s an to me it sounds great ! it sounds good even when its not amped up !

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Dan...

Fender 1987 MIJ Stratocaster, Texas Special Loaded.
Fender 2007 MIA Jazz Deluxe.