Midfielder Bowry and full back Stockley have both decided to extend their stays at Layer Road.
"We are pleased that Sam Stockley has agreed to sign another contract because I feel that he has had an excellent season and, potentially, I believe he could play at a higher level," manager Phil Parkinson (pictured) told the club's official website.
"He has a lot of athleticism, he gives everything in every game he plays and he certainly deserves the offer of a contract.
There were other clubs interested in taking him but I am pleased he has decided to stay with us. I think Sam has made a very good decision in signing another deal with us."
On Bowry, Parkinson added: "We have kept Bob on because he has done very well when he has got in the team towards the end of this season. But that is not the only reason that he was offered a contract.
"Bob's character around the place is absolutely vital to this club and I could not have asked for a better senior pro around the building than Bobby Bowry."
Meanwhile, the club have confirmed that goalkeeper Richard McKinney will not be offered a new contract and can leave the club.
"I have sat down and spoken to Richard about it and we both feel that at this stage in his career he needs to be a team's number one somewhere, at whatever level it is, and I hope it is at Second Division level," said Parkinson.
