Steps creak loud

Need to know how I can fix the creaking of the stairs, without removing the carpet. The carpet is pretty much glued at various places and am afraid if I attempt to take it out, and then screw down the boards, I may not be able to put it back properly in its place, once the job is done.

Any advise will be appreciated.

you could try taking some finish nails and driving them into the 2x12s the stair sits on if you know where they are, then take a nail set and make sure you get the nail below the carpet. I would use a pretty good size nail, just make sure it has the finish nail sized head so that you can punch it through the carpet to hide it.

Welcome Marif:
If the underside of the stairs is acccessible you could 'pressure caulk' (squeezing the glue in the crack while pushing it forward; press at any given place until the adhesive begins to make a bump in front of the nozzle) under the treads with a good construction adhesive such as PL 400. Try to get as much of the adhesive under the treads as possible.
There are several things that can make the stairs that can cause creaking:
loose treads, loose nails in the treads, treads rubbing the wall at their end, treads moving against the risers. Each one has a different remedy.
Glenn

Marif,
Carpet or no carpet, any work to stop squeaking has to be from underneath.

The sketch shows a closed string stair, and yours is probably a cut string, but the principle is the same.
If you have an old stair that squeaks you may be able to fix it by replacing the glue blocks or by simply adding more blocks.
Over the years the old glue perishes.
The glue blocks are essential. Say one for every 300 of width, to the tread to riser joint, and a couple each end at the tread and riser to string joint. They keep the whole structure firm. They stop squeaking in the stair.
You need access to the underside of the stair. Usually it is covered up, so depending on how annoying the squeaks are you may have to remove and later replace the plasterboard or other lining material.
Modern glues like the acrylic stud glue used for fixing plasterboard would be OK, and should last years. Otherwise use a more expensive gap filling epoxy.
Put a blob of glue on each face of the block, push it into position and then slide it along and back an inch or so a few times to expel the air.
Leave the excess glue in place, it all helps.
Glue blocks were used quite a lot in furniture, eg. for fixing drawer bottoms, and they can be replaced in the same way.
Cheers
Bill