Andy's mind is his key resource while in prison.

Andy Dufresne's mind is an important resource throughout his incarceration. From a practical point of view, Andy's mind helps him survive and eventually escape from Shawshank.  Andy was never going to overpower the guards in a swashbuckling manner.  He outsmarted his adversaries.  Andy is able to see how a small rock hammer can get him out of prison.  He is also able to use his smarts as a banker to curry favor with the guards and other inmates. The practical benefits to Andy's mind are extremely important.  

Andy's mindset is also a key resource throughout his time in Shawshank. Andy never loses hope.  Whether it is building a library, helping inmates better themselves, playing Mozart, or simply believing that there is a world outside of prison, Andy's positive outlook is critical.  Andy recognizes that men like Brooks are "institutionalized," being unable to see anything outside of imprisonment.  Andy's commitment to avoid this reality is where his mindset becomes a tremendous resource.  It allows him to both mentally and physically escape.  

Andy is not the strongest or most feared of the inmates at Shawshank. However, he is able to use his mind to survive and eventually triumph over life in prison.