I am doing some tutorials for playing acoustic  blues. I know it's not supposed to be a piece of cake but wondering: is string bendability ( aside from one'side finger strenght) a function of the string type, guitar structure, etc. The bends I see on video seem effortless as if the strings are loose. Mine seem to resist bending with their life!!! My Acoustic is an Alvarez cutaway and strings Elixir, nanoweb lights. Thanks

It's a combination of string thickness and the scale length of the guitar combined with hand strength. I have a video of David Gilmour playing an electric guitar lead on an acoustic. Don't know how he does it but he does use non-standard string gauges. 

A lot of guitarists, especially blues guitarist, tune down a half or even a full step.  This puts less tension on the strings and makes them easier to bend.  Often you need to set up the guitar for that tuning to avoid string buzz.

I would think that metallurgical content and plating/coating would effect elasticity. Metal guitar strings are, after all, complex alloys created for specific properties; I'd guess that elasticity is one of them.
 
If you're doing serious research, I'd contact Dunlop Manufacturing. They manufacture most of the guitar string brands you've ever heard of, and their chief string designer Les O'Connor is a SONAR user. He doesn't stop by the forums much any more, but his online handle was TheStringMaster.

The above hit on everything, I think, but to sum it all up in terms of tension (what you are "fighting" to bend a string):
 
Thinner strings have less tension than thicker for the same note.
Shorter scale length requires less tension for the same note.
Tuning down lessens the tension on the strings by default.
 
Acoustic strings are thicker versus electrics for the same notes, so higher tension; but a couple things to also consider:
 
Heavier strings have better sustain and are louder.
More tension (if rigidly mounted) has better sustain.
Altering a guitar from its designed strings may involve tension rod and/or bridge adjustment, so you can use less tension, but possibly at the expense of string buzzing.
 

For an acoustic guitar, the normal mantra is to use heavier gauge strings than you would for an electric. The heavier the string gauges are, the better the tone tends to be.  However, the trade-off is that you quickly lose the ability to do any sort of meaningful bends.  I have known a few players who used heavy gauge strings on electrics.
I love EB Super slinky .009's on my electric.  A nice balance between tone and bend-ability.  I used them on my acoustic for a while to get that bending thing on it.  However, the tone was weak.  I didn't want to go to heavy on my first acoustic since the neck had been broken and repaired.  I use a heavier gauge string on my Taylor and the tone is impeccable.
 
I read a story many years ago in Guitar Player magazine that in the Nashville studios of the time, they were using really heavy gauge strings to get a classic tone. High E at .015 comes to mind. And.... they were changing the strings after approximately 15 to 20 minutes of playing time since they claimed that the tonal quality of the heavy strings was diminished quickly and noticeably. I don't think I'd be doing that.... but yeah, the heavier gauge strings, to my experience have been harder to bend but the tone quality makes up for what you lose in being able to bend the notes efficiently.
 
All that aside.... one guy on FB who was in the group of musicians I was hanging with back in the day is talking about some strings that are .007 on the high E...... like playing on air..... he says Billy Gibbons is a solid user of that brand.  Dunlop Reverend Willy Extra Lite Guitar Strings... disclaimer... I have not tried them.

- String gauge (obviously heavier gauge strings are harder to bend)
- Pitch - as above, some players tune down a half step to 430, which obviously makes things looser than 440.
- Guitar's scale length - shorter scale lengths are easier to bend than longer
- String types:  steel string will be slightly harder than steel / nickel or bronze.  Pure nickel (more applicable to electric guitars than acoustics) will be a bit easier to bend than a combo of nickel / steel.  Nylon is easier to bend than all the others, but I suspect your question is more aimed at steel strings or steel / bronze for acoustics.
- One additional item others haven't noted yet is frets.  I've found higher frets make sting bending quite a bit easier than guitars with lower frets.
- Hand strength.  When I've gone up to a higher string gauge to get a bigger sound, it's taken me several months of playing almost daily to build up the hand strength (and calluses) to be able to play comfortably.

dwardzala
A lot of guitarists, especially blues guitarist, tune down a half or even a full step.  This puts less tension on the strings and makes them easier to bend.  Often you need to set up the guitar for that tuning to avoid string buzz.

I'm pretty sure this was true for Jimi Hendrix and Stevie Ray.

karma1959
 
- Guitar's scale length - shorter scale lengths are easier to bend than longer
 
- One additional item others haven't noted yet is frets.  I've found higher frets make sting bending quite a bit easier than guitars with lower frets.
 
- Hand strength.  When I've gone up to a higher string gauge to get a bigger sound, it's taken me several months of playing almost daily to build up the hand strength (and calluses) to be able to play comfortably.

I don't think the scale length matters too much. And the frets themselves don't make a difference.  I do think that where... in relation to the fixed ends of the strings, you are trying to bend, makes a huge difference. If you bend in the center of the string..... on the "higher" frets, you have much more elasticity in the strings due to being further from their anchor points at the nut and the bridge, and can push it further out of it's line. Closer to the nut end "on the lower frets"  for example, and its harder to push it off that line. I'm sure there's a better explanation that uses calculus and physics to explain it.
 
And physical hand strength matters a lot.

Fretboard radius affects bending as well. Strings are easier to bend on a flatter fretboard since the string doesn't "choke out" during a bend when the string loses contact with the fret wire as its pushed across the neck.