Can AES in CBC mode be parallelized? Is there any way to parallelize AES running in CBC mode? (The plan is to parallelize it using OpenMP)
Normal CBC mode cannot be parallelized during encryption; that's because CBC mode encryption is defined as:

$$C_i = E_k(C_{i-1} + P_i)$$

That is, what you encrypt during the processing of block $i$ depends on ciphertext of block $i-1$; hence you can't start the next block until you've completed processing of the previous block.  You can't do any parallelization, except for that parallelization that's inherent within AES.

On the other hand, CBC mode in decryption can be parallelized, and it's fairly straightforward.

In addition, there is a variant of CBC mode where you don't xor in the immediately previous ciphertext block, you xor in one $n$ blocks ago, as in:

$$C_i = E_k( C_{i-n} + P_i )$$

This is effectively running $n$ different CBC mode encryptions in parallel; this can be paralleized $n$ ways.