You can use CASTEP. From the CIF file create an input file for CASTEP. I would avoid imposing symmetry, since the elastic tensor is very sensitive to it and the symmetry might break when applying a strain...

Run a full geometry optimization at a suitable level of theory. PBE-D2 or so.

Then use the scripts by Walker and Wilson, a tutorial is available here:

http://www.castep.org/Tutorials/ElasticConstants

I don't know if the full tensor can be computed.

thanks for the answer!

finally appeared some way to solve my problem, but unfortunately, program which you recommend me is paid. Is there any other way to calculate this with free software?

Well, any periodic DFT code would work, but then you cannot use the scripts above.

Check out Quantum Espresso, NWChem, CRYSTAL, VASP.

I use Dmacrys, but that only works for molecular crystals, not MOFs.

thanks again for the answer,

thanks for recommending Dmacrys, it will be also helpful in my research. I will try to use program you suggested.